Chap003 Describing Data Numerical Measures

7/25/2019 Chap003 Describing Data Numerical Measures

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Chapter 03 - Describing Data: Numerical Measures

Chapter 03

Describing Data: Numerical Measures

True / False Questions

1. A value that is typical or representative of the ata is referre to as a measure of centrallocation.!rue "alse

#. !he arithmetic mean is the sum of the $uantitative observations ivie by the total numberof observations.!rue "alse

3. "or a set of ata arrange or sorte in numerical orer% the value of the observation in thecenter is calle the &eighte mean.!rue "alse

'. A set of orinal% interval or ratio level ata may only have one moe.!rue "alse

(. !he moe is the value of the observation that appears most fre$uently.!rue "alse

). *+tremely high or lo& scores affect the value of the meian.!rue "alse

,. !he sum of the eviations from the mean for the set of numbers '% an ( &ill e$ual ero.!rue "alse

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/. !hree persons earn / an hour% si+ earn an hour% an one earns 1# an hour. !he&eighte mean hourly &age is .!rue "alse

. "or any istribution% there are an e$ual number of values above an belo& the mean.!rue "alse

10. !he geometric mean is the nth root of n observations.!rue "alse

11. Dispersion escribes the egree of variation in the ata.!rue "alse

1#. !he mean eviation is the ifference bet&een the mean or the eviations an thearithmetic mean.!rue "alse

13. !he variance is the mean of the sum of the s$uare eviations bet&een each observationan the meian.!rue "alse

1'. !he stanar eviation is the positive s$uare root of the variance.!rue "alse

1(. "or any ata set% Chebyshevs !heorem estimates the proportion of observations thatoccurs &ithin 2 stanar eviations of the mean% &here 2 is greater than 1.0.!rue "alse

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1). n a company% the stanar eviation of the ages of female employees is si+ years an thestanar eviation of the ages of male employees is ten years. !hese statistics inicate that theispersion of age is greater for females than for males.!rue "alse

1,. Accoring to Chebyshevs !heorem% ,(4 percent of the observations lie &ithin plus anminus #.00 average mean eviations.!rue "alse

1/. Accoring to the *mpirical 5ule% ,(4 percent of the observations lie &ithin plus anminus #.00 average mean eviations.

!rue "alse

Multiple Choice Questions

1. !he sum of the eviations of each ata value from this measure of central location &illal&ays be ero.A. Moe6. Mean

C. MeianD. 7tanar eviation

#0. "or any ata set% &hich measures of central location have only one value8A. Moe an meian6. Moe an meanC. Moe an stanar eviationD. Mean an meian

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#1. 9hich measures of central location are not affecte by e+tremely small or e+tremely largevalues8A. Mean an meian6. Mean an moe

C. Moe an meianD. 7tanar eviation an mean

##. 9hat is the relationship among the mean% meian an moe in a symmetric istribution8A. !hey are all e$ual6. !he mean is al&ays the smallest valueC. !he mean is al&ays the largest valueD. !he moe is the largest value

#3. "or a ata set% half of the observations are al&ays greater than theA. Meian6. MoeC. MeanD. 7tanar eviation

#'. 9hat is the lo&est level of measurement that a meian can be compute8

A. Nominal6. rinalC. ntervalD. 5atio

#(. "or a ata set &ith an o number of observations that have been sorte from smallest tolargest values% &here is the meian locate8A. n6. n;#

C. ;#D. n = ?

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#). 9hich one of the follo&ing is referre to as the population mean8A. @6. s

C.

D.

#,. "ifteen accounting maors ha an average grae of 0 on a finance e+am. 7even mar2etingmaors average /(% &hile ten finance maors average 3 on the same e+am. 9hat is the&eighte mean for the 3# stuents ta2ing the e+am8A. /./'6. /.33C. /.'/D. mpossible to etermine &ithout more information

#/. n a survey $uestionnaire% stuents &ere as2e to inicate their class in college. f there&ere only four choices from &hich to choose% &hich measure of central location &oul beappropriate to use for the ata generate by that $uestionnaire item8A. Mean an meian6. Mean an moeC. Moe an meianD. Moe only

#. 9hat is the meian of #)% 30% #'% 3#% 3#% 31% #, an #8A. 3#6. #C. 30D. #.(

30. !he net incomes of a sample of steel fabricators are: /)% ),% /) an /(.

9hat is the moal net income8A. ),6. /(C. /(.(D. /)

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31. A stoc2bro2er place the follo&ing orer for a customer:

(0 shares of Baiser Aluminum preferre at 10' a share

100 shares of !* preferre at #(.#( a share

#0 shares of 6oston *ison preferre at .1#( a share

9hat is the &eighte arithmetic mean price per share8A. #(.#(6. ,.,(C. 103.(0D. ').(1

3#. During the past si+ months% the purchasing agent bought:

9hat is the &eighte arithmetic mean price per ton8A. /,.#(6. ,#.33C. )/.',D. /.1/*. ),.#

33. A sample of single persons receiving social security payments reveale these monthly

benefits: /#)% )% 1%0/,% //0% /3 an )(. o& many observations are belo& themeian8A. 06. 1C. #D. 3*. 3.(

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3'. !he number of &or2 stoppages in a highly inustrialie region for selecte months are: )%0% 10% 1'% / an 0. 9hat is the meian number of stoppages8A. 06. )

C. ,D. /*. 3

3(. Assume a stuent receive the follo&ing graes for the semester: istory% 6E 7tatistics% AE7panish% CE an *nglish% C. istory an *nglish are ( creit hour courses% 7tatistics a ' creithour course an 7panish a 3 creit hour course. f ' grae points are assigne for an A% 3 for a6 an # for a C% &hat is the &eighte mean for the semester graes8A. '.00

6. 1.)C. #.,)D. 3.01

3). A sample of the parameical fees charge by clinics reveale these amounts: ((% '%(0% '(% (# an ((. 9hat is the meian charge8A. ',.(06. (1.00C. (#.00

D. ((.00

3,. !he lengths of time several uner&riters too2 to revie& applications forsimilar insurance coverage are: (0% #30% (# an (,. 9hat is the meian length of timere$uire to revie& an application8A. ('.(6. 1'1.0C. ,.#(D. 10.0

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3/. A bottling company offers three 2ins of elivery service - instant% same ay an &ithinfive ays. !he profit per elivery varies accoring to the 2in of elivery. !he profit for aninstant elivery is less than the other 2ins because the river has to go irectly to a grocerystore &ith a small loa an return to the bottling plant. !o fin out &hat effect each type of

elivery has on the profit picture% the company summarie the ata in the follo&ing tablebase on eliveries for the previous $uarter.

9hat is the &eighte mean profit per elivery8A. ,#

6. 110C. 1'#D. ,*. )).),

3. "or the most recent seven years% the F.7. Department of *ucation reporte the follo&ingnumber of bachelors egrees a&are in computer science: '%033E (%)(#E )%'0,E ,%#01E /%,1E11%1('E 1(%1#1. 9hat is the annual arithmetic mean number of egrees a&are8A. About 1#%#'0

6. About /%3#,C. About )%#1,D. About 1(%)#

'0. A $uestion in a mar2et survey as2s for a responents favorite car color. 9hich measure ofcentral location shoul be use to summarie this $uestion8A. Moe6. MeianC. Mean

D. 7tanar eviation

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'1. 7ometimes% ata has t&o values that have the highest an e$ual fre$uencies. n this case%the istribution of the ata can best be summarie asA. symmetric6. bimoal

C. positively s2e&eD. negatively s2e&e

'#. A isavantage of using an arithmetic mean to summarie a set of ata is that thearithmetic meanA. sometimes has t&o values.6. can be use for interval an ratio ata.C. is al&ays ifferent from the meian.D. can be biase by one or t&o e+tremely small or large values.

'3. !he mean% as a measure of central location &oul be inappropriate for &hich one of thefollo&ing8A. Ages of aults at a senior citien center6. ncomes of la&yersC. Number of pages in te+tboo2s on statisticsD. Marital status of college stuents at a particular university

''. 9hat is a isavantage of the range as a measure of ispersion8A. 6ase on only t&o observations6. Can be istorte by a large meanC. Not in the same units as the original ataD. as no isavantage

'(. 5an2 the measures of ispersion in terms of their relative computational ifficulty fromleast to most.

A. Moe% meian% mean6. 5ange% mean eviation% varianceC. Gariance% mean eviation% rangeD. !here is no ifference

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'). 5an2 the measures of ispersion in terms of their relative ease of interpretation from leastto most.A. Moe% meian% mean6. 5ange% mean eviation% variance

C. Gariance% mean eviation% rangeD. !here is no ifference

',. A purchasing agent for a truc2ing company is shopping for replacement tires for theirtruc2s from t&o suppliers. !he suppliers prices are the same. o&ever% 7upplier As tireshave an average life of )0%000 miles &ith a stanar eviation of 10%000 miles. 7upplier 6stires have an average life of )0%000 miles &ith a stanar eviation of #%000 miles.9hich of the follo&ing statements is true8A. !he t&o istributions of tire life are the same

6. n average% 7upplier As tires have a longer life then 7upplier 6s tiresC. !he life of 7upplier 6s tire is more preictable than the life of 7upplier As tiresD. !he ispersion of 7upplier As tire life is less than the ispersion of 7upplier 6s tire life

'/. !he sum of the ifferences bet&een sample observations an the sample mean isA. Hero6. !he mean eviationC. !he rangeD. !he stanar eviation

'. 9hat is a uni$ue characteristic of the mean eviation8A. t is base on only t&o observations.6. t is base on eviations from the mean.C. t uses absolute values.D. t is only applie to s2e&e istributions.

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(0. f the variance of the Inumber of aily par2ing tic2ets issueI is 100% the variance isefine asA. Inumber of aily par2ing tic2etsI.6. Inumber of aily par2ing tic2etsI s$uare.

C. the absolute value of the Inumber of aily par2ing tic2etsI.D. the s$uare root of the Inumber of aily par2ing tic2etsI.

(1. 9hich of the follo&ing measures of ispersion are base on eviations from the mean8A. Gariance6. 7tanar eviationC. Mean eviationD. All of the above

(#. 9hat is the relationship bet&een the variance an the stanar eviation8A. Gariance is the s$uare root of the stanar eviation6. Gariance is the s$uare of the stanar eviationC. Gariance is t&ice the stanar eviationD. No constant relationship bet&een the variance an the stanar eviation

(3. Accoring to Chebyshevs !heorem% at least &hat percent of the observations lie &ithin

plus an minus 1.,( stanar eviations of the mean8A. ()46. (4C. ),4D. Cannot compute because it epens on the shape of the istribution

('. "or a sample of similar sie all-electric homes% the March electric bills &ere : #1#% 11% 1,)% 1#% 10)% #% 10/% 10% 103% 1#1% 1,( an 1'.9hat is the range8

A. 1006. 130C. 1#0D. 11#

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((. 9hich measure of ispersion isregars the algebraic signs of eachifference bet&een J an the mean8A. 7tanar eviation6. Mean eviation

C. Arithmetic meanD. Gariance

(). !he follo&ing are the &ee2ly amounts of &elfare payments mae by the feeralgovernment to a sample of si+ families: 13% 13)% 130% 13)% 1', an 13). 9hat is therange8A. 06. 1'C. (#

D. 1,

(,. !he &eights of a sample of crates reay for shipment to Mosco&% 5ussia are : 103% ,% 101% 10) an 103. 9hat is the mean eviation8A. 0 2g6. ). 2gC. 10#.0 2gD. #.' 2g*. .0 2g

(/. !he closing prices of a common stoc2 have been )1.(% )#% )1.#(% )0./,( an )1.( for thepast &ee2. 9hat is the range8A. 1.#(06. 1.,(0C. 1.1#(D. 1./,(

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(. !en e+perts rate a ne&ly evelope chocolate chip coo2ie on a scale of 1 to (0. !heirratings &ere: 3'% 3(% '1% #/% #)% #% 3#% 3)% 3/ an '0. 9hat is the mean eviation8A. /.006. '.1#

C. 1#.),D. 0.,(

)0. !he &eights of a group of crates being shippe to Kanama are (% 103% 110%10'% 10(% 11# an #. 9hat is the mean eviation8A. (.'3 2g6. ).#( 2gC. 0.(3 2gD. (#.(0 2g

)1. A sample of the personnel files of eight male employees reveale that% uring a si+-monthperio% they lost the follo&ing number of ays ue to illness: #% 0% )% 3% 10% '% 1 an #. 9hat isthe mean eviation 8A. 16. 0C. 3 1;/D. # 3;/

)#. A sample of the monthly amounts spent for foo by families of four receiving foo stampsappro+imates a symmetrical istribution. !he sample mean is 1(0 an the stanar eviationis #0. Fsing the *mpirical 5ule% about ( percent of the monthly foo e+penitures arebet&een &hat t&o amounts8A. 100 an #006. /( an 10(C. #0( an ##0D. 110 an 10

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)3. !he ages of all the patients in the isolation &ar of the hospital are 3/% #)% 13% '1 an ##.9hat is the population variance8A. 10)./6. 1.'

C. #'0.3D. '#.'

)'. A sample of assistant professors on the business faculty at state supporte institutions inhio reveale the mean income to be ,#%000 for months &ith a stanar eviation of3%000. Fsing Chebyshevs !heorem% &hat proportion of the faculty earns more than ))%000but less than ,/%0008A. At least (046. At least #(4

C. At least ,(4D. At least 1004

)(. A population consists of all the &eights of all efensive tac2les on 7ociable Fniversitysfootball team. !hey are: Lohnson% #0' pounsE Katric2% #1( pounsE Lunior% #0, pounsEBenron% #1# pounsE Nic2o% #1' pounsE an Cochran% #0/ pouns. 9hat is the populationstanar eviation 8A. About '6. About 1)

C. About 100D. About '0

)). !he &eights of the contents of several small bottles are '% #% (% '% (% # an ).9hat is the sample variance8A. ).#6. './0C. 1.)D. #.33

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),. !he istribution of a sample of the outsie iameters of KGC gas pipes appro+imates asymmetrical% bell-shape istribution. !he arithmetic mean is 1'.0 inches% an the stanareviation is 0.1 inches. About )/ percent of the outsie iameters lie bet&een &hat t&oamounts8

A. 13.( an 1'.( inches6. 13.0 an 1(.0 inchesC. 13. an 1'.1 inchesD. 13./ an 1'.# inches

)/. f the sample variance for a fre$uency istribution consisting of hourly &ages &ascompute to be 10% &hat is the sample stanar eviation8A. 1.)6. '.),

C. 3.1)D. 10.00

). 6ase on the *mpirical 5ule% &hat percent of the observations &ill lie bet&een plus orminus t&o stanar eviations from the mean8A. (46. (4C. )/4D. #.(4

,0. 7amples of the &ires coming off the prouction line &ere teste for tensile strength. !hestatistical results &ere:

Accoring to the *mpirical 5ule% the mile ( percent of the &ires teste bet&een

appro+imately &hat t&o values8A. '(0 an ((06. ')0 an ('0C. '#0 an (/0D. 3/0 an )#0

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,1. 9hich measure of central location is use to etermine an average annual percentincrease8A. Arithmetic mean6. 9eighte mean

C. MoeD. eometric mean

,#. !he F.7. "eeral Aviation Aministration reporte that passenger revenues oninternational flights increase from (#/ million in 1/) to (%100 million in #00. 9hat isthe geometric mean annual percent increase in international passenger revenues8A. 10.'6. #,.C. 103.)

D. .)*. #/1'

,3. !he nvestment 5esearch nstitute reporte in its Mutual "un "act 6oo2 that the numberof mutual funs increase from (,#( in 1 to ,,, in #00. 9hat is the geometric meanannual percent increase in the number of funs8A. 1.03'6. 3.3,C. 3.3'

D. ,1.,,*. )33.(

,'. Krouction of passenger cars in Lapan increase from 3.' million in 1 to ).,' millionin #00. 9hat is the geometric mean annual percent increase8A. '.06. 1.C. (.(D. 1).)

*. ',.3

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,(. !he number of stuents at a local university increase from #%(00 stuents to (%000stuents in 10 years. 6ase on a geometric mean% the university gre& at an average percentagerate ofA. #%(00 stuents per year

6. 1.0,1 percent per yearC. ,.1 percent per yearD. #(0 stuents per year

,). n the calculation of the arithmetic mean for groupe ata% &hich value is use torepresent all the values in a particular class8A. !he upper limit of the class.6. !he lo&er limit of the class.C. !he fre$uency of the class.

D. !he cumulative fre$uency preceing the class.*. !he class mipoint.

,,. !he net annual sales of a sample of small retail clothing stores &ere organie into thefollo&ing relative fre$uency istribution.

9hat is the mean net sales 8A. ,.06. 10.0C. /.(D. Mean cannot be compute

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,/. *ach person &ho applies for an assembly ob at 5oberts *lectronics is given a mechanicalaptitue test. ne part of the test involves assembling a plug-in unit base on numbereinstructions. A sample of the length of time it too2 '# persons to assemble the unit &asorganie into the follo&ing fre$uency istribution.

9hat is the stanar eviation 8A. 3./6. ).01C. /.,/

D. 1,.00

Fill in the Blank Questions

,. 9hat measure of central location uses all of the observations in its calculation8

/0. n a fre$uency istribution% &hat measure of central location is use for the class &ith thelargest number of observations8

/1. f a set of observations contains an e+treme value an none of the observations repeatthemselves% &hat is the most representative measure of central location8

/#. !he value that occurs most often in a set of ata is calle the .

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/3. !he &ee2ly sales from a sample of ten computer stores yiele a mean of #(%00E ameian #(%000 an a moe of #'%(00. 9hat is the shape of the istribution8

/'. 9hich measure of central location re$uires that the ata be ran2e before it is possible toetermine it8

/(. A statistic compute by summing all of the values of a istribution an iviing by thenumber of values is calle .

/). f a istribution is highly s2e&e% &hat measure of central location shoul be avoie8

/,. 9hat measure of central location cannot be etermine if the istribution has an open-

ene class8

//. 9hat is the smallest measure of central location in a positively s2e&e istribution8

/. A small manufacturing company &ith (# employees has annual salaries istribute suchthat the mean is #(%'(% the meian is #'%,/ an the moe is #'%000. An aitionalforeman is hire at an annual salary of (0%,00. 9hat measure of central location is mostaffecte by the aition of this salary8

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0. 9hat is the relationship bet&een the mean an meian in a negatively s2e&eistribution8

1. 9hen computing a &eighe mean% the enominator is al&ays .

#. n a epartmental revie& of employee performance% 3 employees &ere score a '% ( employees &ere score a 3 % an 1 employee&as score a 1 . !o compute a &eighte mean% &hat are the&eights8

3. A geometric mean is useful to compute the average percent change over .

'. 9hat is the ifference bet&een the largest an the smallest values in a set of ata8

(. 9hen is the only time the variance e$uals the stanar eviation8

). !he mean absolute eviation is al&ays positive because the numerator computes the.

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,. Accoring to the *mpirical 5ule% &hat percent of the observations lie &ithin plus anminus one stanar eviation of the mean8

/. Chebyshevs !heorem is vali for any .

. 9hat is the positive s$uare root of the variation8

100. 9hat oes the sum of the eviations of each value from the mean e$ual8

101. A company stuie the commissions pai to furniture salespersons. f the variance iscompute% &hat is the unit of measure8

10#. 9hen computing the mean for groupe ata% the numerator is the sum of .

103. A company stuie the commissions pai to furniture salespersons. f the stanareviation is compute% &hat is the unit of measure8

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Short ns!er Questions

10'. A sample reveale that the ages of a popular group of musicians are 3)% #% 3,% 3#% 3)an ,(. 9hat is the meian age8 .

10(. !he istribution of annual salaries for (# employees in a small manufacturing companyhas the follo&ing averages: the mean is #(%'(% the meian is #'%,/ an the moe is#'%000. 9hat is the total amount pai for employee salaries8

10). "ive stuents &ere given a page of problems &ith instructions to solve as many as theycoul in one hour. !he five stuents solve the follo&ing number of problems: 1#% 10% /% )an '. 9hat is the arithmetic mean number of minutes re$uire per problem8 .

10,. !he capacities of several metal containers are: 3/% #0% 3,% )'% an #, liters. 9hat is therange in liters8 .

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10/. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the mean price of Fnleae gas8 .

10. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the mean price of Fnleae Klus gas8 .

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9hat is the mean price of 7uper Fnleae gas8 .


9hat is the meian price of Fnleae gas8 .

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11#. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the meian price of Fnleae Klus gas8 .


9hat is the meian price of 7uper Fnleae gas8 .

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11'. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the moal price of Fnleae gas8 .

11(. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the moal price of Fnleae Klus gas8 .

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11). A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

9hat is the moe8 .

11,. A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

9hat is the arithmetic mean8 .

11/. A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

9hat is the meian8 .

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11. A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

6ase on the values of the arithmetic mean% meian% an moe% &hat is the most li2ely shapeof the istribution8 .

1#0. !he Canal Corporation recore the last five annual percent changes in profit.

9hat is the mean annual percentage change over the last five years8 .

1#1. Coo2 County public safety monitors the number of Iriving uner the influenceI arrestsan is intereste in the istribution of arrests in the month of December over the last ( years.!he ata are

9hat is the sample variance8 .

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1##. Coo2 County public safety monitors the number of Iriving on the influenceI arrests anis intereste in the istribution of arrests in the month of December over the last ( years. !heata are

9hat is the stanar eviation8 .

1#3. !he 7ea Mist otel collects customer satisfaction ata aily. esteray the hotel &as

4 occupie an the manager &ante to $uic2ly assess customer satisfaction. 7he ranomlyselecte ten scores. 100 points is the ma+imum score. !he mean score is /#.1. !he ten scores&ere

9hat is the variance8 .

1#'. !he 7ea Mist otel collects customer satisfaction ata aily. esteray the hotel &as4 occupie an the manager &ante to $uic2ly assess customer satisfaction. 7he ranomlyselecte ten scores. 100 points is the ma+imum score. !he mean score is /#.1. !he ten scores&ere


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1#(. !he mean monthly income of a group of college stuents is (00E the stanar eviationis #0. Accoring to Chebyshevs theorem% at least &hat percent of the incomes &ill liebet&een '00 an )008

1#). !he mean monthly income of a group of college stuents is (00E the stanar eviationis (0. An the mean monthly income is normally istribute. Appro+imately% &hat percent ofthe incomes &ill lie bet&een '00 an )008

1#,. Coastal Carolina Fniversity recently surveye a sample of stuents to etermine ho& farthey live from campus. !he results are sho&n belo&. Compute the mean istance.

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1#/. Coastal Carolina Fniversity recently surveye a sample of stuents to etermine ho& farthey live from campus. !he results are sho&n belo&. Compute the stanar eviation.

"ssa# Questions

1#. 9hat are the similarities an ifferences bet&een the mean% the meian% an the moe8

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130. 9hat are the similarities an ifferences bet&een the range an the stanar eviation8

131. 9hen reporting escriptive statistics for a variable% &hy shoul the report incluemeasures of location an ispersion8

13#. 9hat are the similarities an ifferences bet&een the applications of Chebyshevs!heorem an the *mpirical 5ule8

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Chapter 03 Describing Data: Numerical Measures Ans&er Bey

True / False Questions

1. A value that is typical or representative of the ata is referre to as a measure of centrallocation.T$%"

AACSB: Communication Abilities

Bloom's: KnowledgeDifficulty: Easy

Learning Objectie: !"#!$ E%&lain te conce&t of central tendency(

)o&ic: Conce&t of Central )endency

#. !he arithmetic mean is the sum of the $uantitative observations ivie by the total numberof observations.T$%"


Bloom's: Knowledge

Difficulty: Easy

Learning Objectie: !"#!* +dentify and com&ute te aritmetic mean()o&ic: Aritmetic ,ean

3. "or a set of ata arrange or sorte in numerical orer% the value of the observation in thecenter is calle the &eighte mean.F&S"


Bloom's: Knowledge

Difficulty: Easy

Learning Objectie: !"#!" Com&ute and inter&ret te weigted mean()o&ic: -eigted ,ean

3-33


34/79


'. A set of orinal% interval or ratio level ata may only have one moe.F&S"

AACSB: .eflectie )in/ing

Bloom's: A&&lication

Difficulty: Easy

Learning Objectie: !"#!0 +dentify te mode()o&ic: )e ,ode

(. !he moe is the value of the observation that appears most fre$uently.T$%"

AACSB: Communication AbilitiesBloom's: Knowledge

Difficulty: Easy

Learning Objectie: !"#!0 +dentify te mode(

)o&ic: )e ,ode

). *+tremely high or lo& scores affect the value of the meian.F&S"


Bloom's: Com&reension

Difficulty: Easy

Learning Objectie: !"#!1 Determine te median()o&ic: )e ,edian

3-3'


35/79


,. !he sum of the eviations from the mean for the set of numbers '% an ( &ill e$ual ero.T$%"

AACSB: Analytic S/ills


Difficulty: Easy


/. !hree persons earn / an hour% si+ earn an hour% an one earns 1# an hour. !he&eighte mean hourly &age is .T$%"



Difficulty: ,edium


. "or any istribution% there are an e$ual number of values above an belo& the mean.F&S"


Bloom's: Com&reensionDifficulty: Easy

Learning Objectie: !"#!1 Determine te median(

)o&ic: )e ,edian

3-3(


36/79


10. !he geometric mean is the nth root of n observations.T$%"


Bloom's: Knowledge

Difficulty: ,edium

Learning Objectie: !"#!2 Calculate te geometric mean()o&ic: 3eometric ,ean

11. Dispersion escribes the egree of variation in the ata.T$%"



Learning Objectie: !"#!4 E%&lain and a&&ly measures of dis&ersion(

)o&ic: ,easures of Dis&ersion

1#. !he mean eviation is the ifference bet&een the mean or the eviations an thearithmetic mean.F&S"


Bloom's: Knowledge

Difficulty: ,ediumLearning Objectie: !"#!4 E%&lain and a&&ly measures of dis&ersion(


13. !he variance is the mean of the sum of the s$uare eviations bet&een each observationan the meian.F&S"


Bloom's: Knowledge

Difficulty: ,ediumLearning Objectie: !"#!5 Com&ute and e%&lain te ariance and te standard deiation()o&ic: 6ariance and Standard Deiation

3-3)


37/79


1'. !he stanar eviation is the positive s$uare root of the variance.T$%"


Bloom's: Knowledge

Difficulty: ,edium

Learning Objectie: !"#!5 Com&ute and e%&lain te ariance and te standard deiation()o&ic: 6ariance and Standard Deiation

1(. "or any ata set% Chebyshevs !heorem estimates the proportion of observations thatoccurs &ithin 2 stanar eviations of the mean% &here 2 is greater than 1.0.T$%"


Difficulty: ,edium

Learning Objectie: !"#!7 E%&lain Cebyse's )eorem and te Em&irical .ule(

)o&ic: 8ses of te Standard Deiation

1). n a company% the stanar eviation of the ages of female employees is si+ years an thestanar eviation of the ages of male employees is ten years. !hese statistics inicate that theispersion of age is greater for females than for males.F&S"


Bloom's: Analysis

Difficulty: Easy



1,. Accoring to Chebyshevs !heorem% ,(4 percent of the observations lie &ithin plus anminus #.00 average mean eviations.F&S"

AACSB: Communication AbilitiesBloom's: Com&reension

Difficulty: Easy



3-3,


38/79


1/. Accoring to the *mpirical 5ule% ,(4 percent of the observations lie &ithin plus anminus #.00 average mean eviations.F&S"





Multiple Choice Questions

1. !he sum of the eviations of each ata value from this measure of central location &ill

al&ays be ero.A.MoeB'MeanC.MeianD.7tanar eviation



Learning Objectie: !"#!* +dentify and com&ute te aritmetic mean(

)o&ic: Aritmetic ,ean

#0. "or any ata set% &hich measures of central location have only one value8A.Moe an meian6.Moe an meanC.Moe an stanar eviationD'Mean an meian



Difficulty: Easy

Learning Objectie: !"#!$ E%&lain te conce&t of central tendency()o&ic: Conce&t of Central )endency

3-3/


39/79


#1. 9hich measures of central location are not affecte by e+tremely small or e+tremely largevalues8A.Mean an meian6.Mean an moe

C'Moe an meianD.7tanar eviation an mean



Difficulty: EasyLearning Objectie: !"#!$ E%&lain te conce&t of central tendency(


##. 9hat is the relationship among the mean% meian an moe in a symmetric istribution8

'!hey are all e$ual6.!he mean is al&ays the smallest valueC.!he mean is al&ays the largest valueD.!he moe is the largest value

AACSB: Communication AbilitiesBloom's: A&&lication

Difficulty: Easy


)o&ic: .elatie 9ositions of te ,ean ,edian and ,ode

#3. "or a ata set% half of the observations are al&ays greater than the'Meian6.MoeC.MeanD.7tanar eviation


Bloom's: Knowledge

Difficulty: Easy


3-3


40/79


#'. 9hat is the lo&est level of measurement that a meian can be compute8A.NominalB'rinalC.nterval

D.5atio



Difficulty: ,edium


#(. "or a ata set &ith an o number of observations that have been sorte from smallest tolargest values% &here is the meian locate8

A.n6.n;#C';#D.n = ?

AACSB: Analytic S/illsBloom's: Com&reension

Difficulty: ,edium


)o&ic: )e ,edian

#). 9hich one of the follo&ing is referre to as the population mean8'@6.s

C.

D.


Bloom's: Knowledge

Difficulty: ,edium


)o&ic: 9o&ulation ,ean

3-'0


41/79


#,. "ifteen accounting maors ha an average grae of 0 on a finance e+am. 7even mar2etingmaors average /(% &hile ten finance maors average 3 on the same e+am. 9hat is the&eighte mean for the 3# stuents ta2ing the e+am8'/./'

6./.33C./.'/D.mpossible to etermine &ithout more information

AACSB: Analytic S/illsBloom's: A&&lication

Difficulty: ,edium

Learning Objectie: !"#!" Com&ute and inter&ret te weigted mean(

)o&ic: -eigted ,ean

#/. n a survey $uestionnaire% stuents &ere as2e to inicate their class in college. f there&ere only four choices from &hich to choose% &hich measure of central location &oul beappropriate to use for the ata generate by that $uestionnaire item8A.Mean an meian6.Mean an moeC'Moe an meianD.Moe only

AACSB: .eflectie )in/ingBloom's: A&&lication

Difficulty: ,edium

Learning Objectie: !"#!$ E%&lain te conce&t of central tendency()o&ic: Conce&t of Central )endency

#. 9hat is the meian of #)% 30% #'% 3#% 3#% 31% #, an #8A.3#6.#C.30D'#.(


Difficulty: ,edium


3-'1


42/79


30. !he net incomes of a sample of steel fabricators are: /)% ),% /) an /(.9hat is the moal net income8A.),6./(

C./(.(D'/)



Difficulty: EasyLearning Objectie: !"#!0 +dentify te mode(

)o&ic: )e ,ode

31. for a customer:

(0 shares of Baiser Aluminum preferre at 10' a share100 shares of !* preferre at #(.#( a share

#0 shares of 6oston *ison preferre at .1#( a share

9hat is the &eighte arithmetic mean price per share8A.#(.#(6.,.,(C.103.(0D'').(1


Bloom's: A&&licationDifficulty: ;ard


)o&ic: -eigted ,ean

3-'#


43/79


3#. During the past si+ months% the purchasing agent bought:

9hat is the &eighte arithmetic mean price per ton8A./,.#(B',#.33C.)/.',D./.1/*.),.#



Difficulty: ;ard


)o&ic: -eigted ,ean

33. A sample of single persons receiving social security payments reveale these monthlybenefits: /#)% )% 1%0/,% //0% /3 an )(. o& many observations are belo& themeian8A.06.1C.#D'3*.3.(



Difficulty: ,ediumLearning Objectie: !"#!1 Determine te median(

)o&ic: )e ,edian

3-'3


44/79


3'. !he number of &or2 stoppages in a highly inustrialie region for selecte months are: )%0% 10% 1'% / an 0. 9hat is the meian number of stoppages8A.06.)

C',D./*.3


Difficulty: ,edium


)o&ic: )e ,edian

3(. Assume a stuent receive the follo&ing graes for the semester: istory% 6E 7tatistics% AE7panish% CE an *nglish% C. istory an *nglish are ( creit hour courses% 7tatistics a ' creithour course an 7panish a 3 creit hour course. f ' grae points are assigne for an A% 3 for a6 an # for a C% &hat is the &eighte mean for the semester graes8A.'.006.1.)C'#.,)D.3.01



Difficulty: ;ard


)o&ic: -eigted ,ean

3). A sample of the parameical fees charge by clinics reveale these amounts: ((% '%(0% '(% (# an ((. 9hat is the meian charge8A.',.(0B'(1.00C.(#.00D.((.00


Difficulty: ;ard


)o&ic: )e ,edian

3-''


45/79


3,. !he lengths of time several uner&riters too2 to revie& applications forsimilar insurance coverage are: (0% #30% (# an (,. 9hat is the meian length of timere$uire to revie& an application8'('.(

6.1'1.0C.,.#(D.10.0


Difficulty: ;ard


)o&ic: )e ,edian

3/. A bottling company offers three 2ins of elivery service - instant% same ay an &ithinfive ays. !he profit per elivery varies accoring to the 2in of elivery. !he profit for aninstant elivery is less than the other 2ins because the river has to go irectly to a grocerystore &ith a small loa an return to the bottling plant. !o fin out &hat effect each type ofelivery has on the profit picture% the company summarie the ata in the follo&ing tablebase on eliveries for the previous $uarter.

9hat is the &eighte mean profit per elivery8A.,#6.110C.1'#D',*.)).),




3-'(


46/79


3. "or the most recent seven years% the F.7. Department of *ucation reporte the follo&ingnumber of bachelors egrees a&are in computer science: '%033E (%)(#E )%'0,E ,%#01E /%,1E11%1('E 1(%1#1. 9hat is the annual arithmetic mean number of egrees a&are8A.About 1#%#'0

B'About /%3#,C.About )%#1,D.About 1(%)#


Difficulty: ;ard



'0. A $uestion in a mar2et survey as2s for a responents favorite car color. 9hich measure ofcentral location shoul be use to summarie this $uestion8'Moe6.MeianC.MeanD.7tanar eviation




)o&ic: )e ,ode

'1. 7ometimes% ata has t&o values that have the highest an e$ual fre$uencies. n this case%the istribution of the ata can best be summarie asA.symmetricB'bimoal C.positively s2e&eD.negatively s2e&e


Difficulty: ,edium


3-')


47/79


'#. A isavantage of using an arithmetic mean to summarie a set of ata is that thearithmetic meanA.sometimes has t&o values.6.can be use for interval an ratio ata.

C.is al&ays ifferent from the meian.D'can be biase by one or t&o e+tremely small or large values.



Difficulty: EasyLearning Objectie: !"#!* +dentify and com&ute te aritmetic mean(


'3. !he mean% as a measure of central location &oul be inappropriate for &hich one of the

follo&ing8A.Ages of aults at a senior citien center6.ncomes of la&yersC.Number of pages in te+tboo2s on statisticsD'Marital status of college stuents at a particular university



Difficulty: ,edium


''. 9hat is a isavantage of the range as a measure of ispersion8'6ase on only t&o observations6.Can be istorte by a large meanC.Not in the same units as the original ataD.as no isavantage



Difficulty: Easy

Learning Objectie: !"#!4 E%&lain and a&&ly measures of dis&ersion()o&ic: ,easures of Dis&ersion

3-',


48/79


'(. 5an2 the measures of ispersion in terms of their relative computational ifficulty fromleast to most.A.Moe% meian% meanB'5ange% mean eviation% variance

C.Gariance% mean eviation% rangeD.!here is no ifference


Bloom's: Analysis

Difficulty: EasyLearning Objectie: !"#!4 E%&lain and a&&ly measures of dis&ersion(


'). 5an2 the measures of ispersion in terms of their relative ease of interpretation from least

to most.A.Moe% meian% meanB'5ange% mean eviation% varianceC.Gariance% mean eviation% rangeD.!here is no ifference


Bloom's: Analysis

Difficulty: Easy


',. A purchasing agent for a truc2ing company is shopping for replacement tires for theirtruc2s from t&o suppliers. !he suppliers prices are the same. o&ever% 7upplier As tireshave an average life of )0%000 miles &ith a stanar eviation of 10%000 miles. 7upplier 6stires have an average life of )0%000 miles &ith a stanar eviation of #%000 miles.9hich of the follo&ing statements is true8A.!he t&o istributions of tire life are the same6.n average% 7upplier As tires have a longer life then 7upplier 6s tiresC'!he life of 7upplier 6s tire is more preictable than the life of 7upplier As tiresD.!he ispersion of 7upplier As tire life is less than the ispersion of 7upplier 6s tire life

AACSB: .eflectie )in/ingBloom's: Analysis

Difficulty: ,edium



3-'/


49/79


'/. !he sum of the ifferences bet&een sample observations an the sample mean is'Hero6.!he mean eviationC.!he range

D.!he stanar eviation



Difficulty: Easy


'. 9hat is a uni$ue characteristic of the mean eviation8A.t is base on only t&o observations.

6.t is base on eviations from the mean.C't uses absolute values.D.t is only applie to s2e&e istributions.


Bloom's: Com&reensionDifficulty: ,edium



(0. f the variance of the Inumber of aily par2ing tic2ets issueI is 100% the variance is

efine asA.Inumber of aily par2ing tic2etsI.B'Inumber of aily par2ing tic2etsI s$uare.C.the absolute value of the Inumber of aily par2ing tic2etsI.D.the s$uare root of the Inumber of aily par2ing tic2etsI.



Difficulty: ,edium

Learning Objectie: !"#!5 Com&ute and e%&lain te ariance and te standard deiation()o&ic: 6ariance and Standard Deiation

3-'


50/79


(1. 9hich of the follo&ing measures of ispersion are base on eviations from the mean8A.Gariance6.7tanar eviationC.Mean eviation

D'All of the above


Bloom's: Knowledge

Difficulty: ,edium


(#. 9hat is the relationship bet&een the variance an the stanar eviation8A.Gariance is the s$uare root of the stanar eviation

B'Gariance is the s$uare of the stanar eviationC.Gariance is t&ice the stanar eviationD.No constant relationship bet&een the variance an the stanar eviation



Learning Objectie: !"#!5 Com&ute and e%&lain te ariance and te standard deiation(

)o&ic: 6ariance and Standard Deiation

(3. Accoring to Chebyshevs !heorem% at least &hat percent of the observations lie &ithin

plus an minus 1.,( stanar eviations of the mean8A.()46.(4C'),4D.Cannot compute because it epens on the shape of the istribution



Difficulty: ,edium

Learning Objectie: !"#!7 E%&lain Cebyse's )eorem and te Em&irical .ule()o&ic: 8ses of te Standard Deiation

3-(0


51/79


('. "or a sample of similar sie all-electric homes% the March electric bills &ere : #1#% 11% 1,)% 1#% 10)% #% 10/% 10% 103% 1#1% 1,( an 1'.9hat is the range8A.100

6.130C'1#0D.11#


Difficulty: Easy



((. 9hich measure of ispersion isregars the algebraic signs of eachifference bet&een J an the mean8A.7tanar eviationB'Mean eviationC.Arithmetic meanD.Gariance





(). !he follo&ing are the &ee2ly amounts of &elfare payments mae by the feeralgovernment to a sample of si+ families: 13% 13)% 130% 13)% 1', an 13). 9hat is therange8A.06.1'C.(#D'1,





3-(1


52/79


(,. !he &eights of a sample of crates reay for shipment to Mosco&% 5ussia are : 103% ,% 101% 10) an 103. 9hat is the mean eviation8A.0 2g6.). 2g

C.10#.0 2gD'#.' 2g*..0 2g


Difficulty: ,edium



(/. !he closing prices of a common stoc2 have been )1.(% )#% )1.#(% )0./,( an )1.( for thepast &ee2. 9hat is the range8A.1.#(06.1.,(0C'1.1#(D.1./,(





(. !en e+perts rate a ne&ly evelope chocolate chip coo2ie on a scale of 1 to (0. !heirratings &ere: 3'% 3(% '1% #/% #)% #% 3#% 3)% 3/ an '0. 9hat is the mean eviation8A./.00B''.1#C.1#.),D.0.,(


Difficulty: ,edium


3-(#


53/79


)0. !he &eights of a group of crates being shippe to Kanama are (% 103% 110%10'% 10(% 11# an #. 9hat is the mean eviation8'(.'3 2g6.).#( 2g

C.0.(3 2gD.(#.(0 2g





)1. A sample of the personnel files of eight male employees reveale that% uring a si+-month

perio% they lost the follo&ing number of ays ue to illness: #% 0% )% 3% 10% '% 1 an #. 9hat isthe mean eviation 8A.16.0C.3 1;/D'# 3;/





)#. A sample of the monthly amounts spent for foo by families of four receiving foo stampsappro+imates a symmetrical istribution. !he sample mean is 1(0 an the stanar eviationis #0. Fsing the *mpirical 5ule% about ( percent of the monthly foo e+penitures arebet&een &hat t&o amounts8A.100 an #006./( an 10(C.#0( an ##0D'110 an 10


Difficulty: ,edium



3-(3


54/79


)3. !he ages of all the patients in the isolation &ar of the hospital are 3/% #)% 13% '1 an ##.9hat is the population variance8'10)./6.1.'

C.#'0.3D.'#.'



Difficulty: ,ediumLearning Objectie: !"#!5 Com&ute and e%&lain te ariance and te standard deiation(


)'. A sample of assistant professors on the business faculty at state supporte institutions in

hio reveale the mean income to be ,#%000 for months &ith a stanar eviation of3%000. Fsing Chebyshevs !heorem% &hat proportion of the faculty earns more than ))%000but less than ,/%0008A.At least (046.At least #(4C'At least ,(4D.At least 1004


Difficulty: ,edium


)(. A population consists of all the &eights of all efensive tac2les on 7ociable Fniversitysfootball team. !hey are: Lohnson% #0' pounsE Katric2% #1( pounsE Lunior% #0, pounsEBenron% #1# pounsE Nic2o% #1' pounsE an Cochran% #0/ pouns. 9hat is the populationstanar eviation 8'About '6.About 1)C.About 100D.About '0



Difficulty: ,edium



3-('


55/79


)). !he &eights of the contents of several small bottles are '% #% (% '% (% # an ).9hat is the sample variance8A.).#6.'./0

C.1.)D'#.33





),. !he istribution of a sample of the outsie iameters of KGC gas pipes appro+imates a

symmetrical% bell-shape istribution. !he arithmetic mean is 1'.0 inches% an the stanareviation is 0.1 inches. About )/ percent of the outsie iameters lie bet&een &hat t&oamounts8A.13.( an 1'.( inches6.13.0 an 1(.0 inchesC'13. an 1'.1 inchesD.13./ an 1'.# inches


Difficulty: ,edium


)/. f the sample variance for a fre$uency istribution consisting of hourly &ages &ascompute to be 10% &hat is the sample stanar eviation8A.1.)6.'.),C'3.1)D.10.00





3-((


56/79


). 6ase on the *mpirical 5ule% &hat percent of the observations &ill lie bet&een plus orminus t&o stanar eviations from the mean8'(46.(4

C.)/4D.#.(4



Difficulty: ;ardLearning Objectie: !"#!7 E%&lain Cebyse's )eorem and te Em&irical .ule(


,0. 7amples of the &ires coming off the prouction line &ere teste for tensile strength. !he

statistical results &ere:

Accoring to the *mpirical 5ule% the mile ( percent of the &ires teste bet&eenappro+imately &hat t&o values8A.'(0 an ((06.')0 an ('0C''#0 an (/0D.3/0 an )#0



Difficulty: ,edium


3-()


57/79


,1. 9hich measure of central location is use to etermine an average annual percentincrease8A.Arithmetic mean6.9eighte mean

C.MoeD'eometric mean



Difficulty: EasyLearning Objectie: !"#!2 Calculate te geometric mean(

)o&ic: 3eometric ,ean

,#. !he F.7. "eeral Aviation Aministration reporte that passenger revenues on

international flights increase from (#/ million in 1/) to (%100 million in #00. 9hat isthe geometric mean annual percent increase in international passenger revenues8'10.'6.#,.C.103.)D..)*.#/1'


Difficulty: ;ard


,3. !he nvestment 5esearch nstitute reporte in its Mutual "un "act 6oo2 that the numberof mutual funs increase from (,#( in 1 to ,,, in #00. 9hat is the geometric meanannual percent increase in the number of funs8A.1.03'B'3.3,C.3.3'D.,1.,,*.)33.(



Difficulty: ;ard

Learning Objectie: !"#!2 Calculate te geometric mean(


3-(,


58/79


,'. Krouction of passenger cars in Lapan increase from 3.' million in 1 to ).,' millionin #00. 9hat is the geometric mean annual percent increase8A.'.06.1.

C'(.(D.1).)*.',.3


Difficulty: ;ard



,(. !he number of stuents at a local university increase from #%(00 stuents to (%000stuents in 10 years. 6ase on a geometric mean% the university gre& at an average percentagerate ofA.#%(00 stuents per year6.1.0,1 percent per yearC',.1 percent per yearD.#(0 stuents per year


Difficulty: ;ard


,). n the calculation of the arithmetic mean for groupe ata% &hich value is use torepresent all the values in a particular class8A.!he upper limit of the class.6.!he lo&er limit of the class.C.!he fre$uency of the class.D.!he cumulative fre$uency preceing the class."'!he class mipoint.


Difficulty: ,edium

Learning Objectie: !"#$! Com&ute te mean and standard deiation of grou&ed data(

)o&ic: ,ean and Standard Deiation of 3rou&ed data

3-(/


59/79


,,. !he net annual sales of a sample of small retail clothing stores &ere organie into thefollo&ing relative fre$uency istribution.

9hat is the mean net sales 8A.,.06.10.0C./.(D'Mean cannot be compute



Difficulty: ;ard

Learning Objectie: !"#$! Com&ute te mean and standard deiation of grou&ed data()o&ic: ,ean and Standard Deiation of 3rou&ed data

3-(


60/79


,/. *ach person &ho applies for an assembly ob at 5oberts *lectronics is given a mechanicalaptitue test. ne part of the test involves assembling a plug-in unit base on numbereinstructions. A sample of the length of time it too2 '# persons to assemble the unit &asorganie into the follo&ing fre$uency istribution.

9hat is the stanar eviation 8'3./6.).01C./.,/

D.1,.00


Difficulty: ,edium



Fill in the Blank Questions

,. 9hat measure of central location uses all of the observations in its calculation8Mean


Bloom's: Knowledge

Difficulty: Easy


3-)0


61/79


/0. n a fre$uency istribution% &hat measure of central location is use for the class &ith thelargest number of observations8 Mo(e




)o&ic: )e ,ode

/1. f a set of observations contains an e+treme value an none of the observations repeatthemselves% &hat is the most representative measure of central location8 Me(ian




)o&ic: )e ,edian

/#. !he value that occurs most often in a set of ata is calle the .Mo(e


Difficulty: Easy


)o&ic: )e ,ode

/3. !he &ee2ly sales from a sample of ten computer stores yiele a mean of #(%00E ameian #(%000 an a moe of #'%(00. 9hat is the shape of the istribution8)ositi*el# ske!e(

AACSB: .eflectie )in/ingBloom's: Com&reension

Difficulty: ,edium



3-)1


62/79


/'. 9hich measure of central location re$uires that the ata be ran2e before it is possible toetermine it8 Me(ian


Bloom's: KnowledgeDifficulty: ,edium


)o&ic: )e ,edian

/(. A statistic compute by summing all of the values of a istribution an iviing by thenumber of values is calle .arithmetic mean


Bloom's: Knowledge

Difficulty: ,ediumLearning Objectie: !"#!* +dentify and com&ute te aritmetic mean(


/). f a istribution is highly s2e&e% &hat measure of central location shoul be avoie8Mean



Difficulty: ,edium



/,. 9hat measure of central location cannot be etermine if the istribution has an open-ene class8 rithmetic mean


Difficulty: ,edium



3-)#


63/79


//. 9hat is the smallest measure of central location in a positively s2e&e istribution8Mo(e




)o&ic: )e ,ode

/. A small manufacturing company &ith (# employees has annual salaries istribute suchthat the mean is #(%'(% the meian is #'%,/ an the moe is #'%000. An aitionalforeman is hire at an annual salary of (0%,00. 9hat measure of central location is mostaffecte by the aition of this salary8

rithmetic mean


Bloom's: Analysis

Difficulty: ,edium



0. 9hat is the relationship bet&een the mean an meian in a negatively s2e&eistribution8 Mean is less than the me(ian





1. 9hen computing a &eighe mean% the enominator is al&ays .the sum o+ the !eights



Difficulty: ,edium


3-)3


64/79


#. n a epartmental revie& of employee performance% 3 employees &ere score a '% ( employees &ere score a 3 % an 1 employee&as score a 1 . !o compute a &eighte mean% &hat are the&eights8

3, -, an( . emplo#ees



Difficulty: ,edium


3. A geometric mean is useful to compute the average percent change over .time





'. 9hat is the ifference bet&een the largest an the smallest values in a set of ata8$ange


Bloom's: Knowledge



(. 9hen is the only time the variance e$uals the stanar eviation8 Both eual .


Difficulty: ,edium



3-)'


65/79


). !he mean absolute eviation is al&ays positive because the numerator computes the.absolute *alue o+ the (e*iations +rom the sample mean


Bloom's: Com&reensionDifficulty: ;ard



,. Accoring to the *mpirical 5ule% &hat percent of the observations lie &ithin plus anminus one stanar eviation of the mean8 12



Difficulty: ,ediumLearning Objectie: !"#!7 E%&lain Cebyse's )eorem and te Em&irical .ule(


/. Chebyshevs !heorem is vali for any .(istribution

AACSB: .eflectie )in/ingBloom's: Com&reension

Difficulty: ,edium



. 9hat is the positive s$uare root of the variation8 Stan(ar( (e*iation



Difficulty: EasyLearning Objectie: !"#!5 Com&ute and e%&lain te ariance and te standard deiation()o&ic: 6ariance and Standard Deiation

3-)(


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100. 9hat oes the sum of the eviations of each value from the mean e$ual8ero





101. A company stuie the commissions pai to furniture salespersons. f the variance iscompute% &hat is the unit of measure8 Dollars suare(





10#. 9hen computing the mean for groupe ata% the numerator is the sum of .the pro(uct o+ class +reuencies an( mi(points

AACSB: Analytic S/illsBloom's: Com&reension

Difficulty: ,edium



103. A company stuie the commissions pai to furniture salespersons. f the stanareviation is compute% &hat is the unit of measure8 Dollars





3-))


67/79


Short ns!er Questions

10'. A sample reveale that the ages of a popular group of musicians are 3)% #% 3,% 3#% 3)an ,(. 9hat is the meian age8 .

3)




)o&ic: )e ,edian

10(. !he istribution of annual salaries for (# employees in a small manufacturing companyhas the follo&ing averages: the mean is #(%'(% the meian is #'%,/ an the moe is

#'%000. 9hat is the total amount pai for employee salaries8

1%3#3%/)/


Bloom's: Analysis

Difficulty: ;ard


10). "ive stuents &ere given a page of problems &ith instructions to solve as many as theycoul in one hour. !he five stuents solve the follo&ing number of problems: 1#% 10% /% )an '. 9hat is the arithmetic mean number of minutes re$uire per problem8 .

,.( minutes



Difficulty: ;ardLearning Objectie: !"#!* +dentify and com&ute te aritmetic mean(


3-),


68/79


10,. !he capacities of several metal containers are: 3/% #0% 3,% )'% an #, liters. 9hat is therange in liters8 .

'' liters


Bloom's: A&&licationDifficulty: Easy



10/. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the mean price of Fnleae gas8 .

#.#,


Difficulty: Easy



3-)/


69/79



9hat is the mean price of Fnleae Klus gas8 .

#.3/


Difficulty: ,edium




9hat is the mean price of 7uper Fnleae gas8 .

#.(#



Difficulty: ,edium


3-)


70/79


71/79



9hat is the meian price of 7uper Fnleae gas8 .

#.(0


Difficulty: Easy


)o&ic: )e ,edian

11'. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the moal price of Fnleae gas8 .

#.#,



Difficulty: Easy


3-,1


72/79


11(. A sample of five full service gasoline stations% each carrying three graes of gasoline%&as ta2en an the price per liter &as recore for each grae of gasoline%as sho&n in the table belo&.

9hat is the moal price of Fnleae Klus gas8 .

#.3/



Difficulty: ,edium


)o&ic: )e ,ode

11). A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

9hat is the moe8 .

#1




)o&ic: )e ,ode

3-,#


73/79


11,. A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

9hat is the arithmetic mean8 .

#0.3)


Bloom's: A&&licationDifficulty: Easy



11/. A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

9hat is the meian8 .

#1


Difficulty: Easy


11. A companys human resource epartment &as intereste in the average number of yearsthat a person &or2s before retiring. !he sample of sie 11 follo&s:

6ase on the values of the arithmetic mean% meian% an moe% &hat is the most li2ely shapeof the istribution8 .

7ymmetric


Bloom's: Analysis

Difficulty: ;ard



3-,3


74/79


1#0. !he Canal Corporation recore the last five annual percent changes in profit.

9hat is the mean annual percentage change over the last five years8 .

,./4


Difficulty: ;ard



1#1. Coo2 County public safety monitors the number of Iriving uner the influenceI arrestsan is intereste in the istribution of arrests in the month of December over the last ( years.!he ata are

9hat is the sample variance8 .

11).#


Difficulty: ;ard



3-,'


75/79


1##. Coo2 County public safety monitors the number of Iriving on the influenceI arrests anis intereste in the istribution of arrests in the month of December over the last ( years. !heata are


10.,,)



Difficulty: ;ard



1#3. !he 7ea Mist otel collects customer satisfaction ata aily. esteray the hotel &as4 occupie an the manager &ante to $uic2ly assess customer satisfaction. 7he ranomlyselecte ten scores. 100 points is the ma+imum score. !he mean score is /#.1. !he ten scores&ere

9hat is the variance8 .

#)#.('''





3-,(


76/79


1#'. !he 7ea Mist otel collects customer satisfaction ata aily. esteray the hotel &as4 occupie an the manager &ante to $uic2ly assess customer satisfaction. 7he ranomlyselecte ten scores. 100 points is the ma+imum score. !he mean score is /#.1. !he ten scores&ere


1).#03#





1#(. !he mean monthly income of a group of college stuents is (00E the stanar eviationis #0. Accoring to Chebyshevs theorem% at least &hat percent of the incomes &ill liebet&een '00 an )008

,(4




1#). !he mean monthly income of a group of college stuents is (00E the stanar eviationis (0. An the mean monthly income is normally istribute. Appro+imately% &hat percent ofthe incomes &ill lie bet&een '00 an )008

(4

AACSB: Analytic S/illsBloom's: A&&licationDifficulty: ;ard



3-,)


77/79


1#,. Coastal Carolina Fniversity recently surveye a sample of stuents to etermine ho& farthey live from campus. !he results are sho&n belo&. Compute the mean istance.

1#.)1111





1#/. Coastal Carolina Fniversity recently surveye a sample of stuents to etermine ho& farthey live from campus. !he results are sho&n belo&. Compute the stanar eviation.

(./1



Difficulty: ;ardLearning Objectie: !"#$! Com&ute te mean and standard deiation of grou&ed data(


3-,,


78/79


"ssa# Questions

1#. 9hat are the similarities an ifferences bet&een the mean% the meian% an the moe8

Ans&ers may vary but shoul inclue the follo&ing points. 9hile all are measures of aistributions central location% each is compute an interprete ifferently. !he mean is theaverage of all values in a ata set. ts value is affecte by e+treme values inthe ata set. n this case% the mean is probably not a goo measure of a istributions centrallocation. !he meian is also a measure of central location. o&ever% its value is etermineby sorting or arranging ata in orer an then fining the value in the mile of the sorte list.!herefore% (04 of all ata set values are less than the meian% an (04 are greater than themeian. !he meian is not affecte by e+treme values in a ataset. !he moe is the value in aataset that has the highest fre$uency. 7ometimes a ata set may have more than one moebecause more than one value has the highest an e$ual fre$uency.


Difficulty: ,edium



130. 9hat are the similarities an ifferences bet&een the range an the stanar eviation8

6oth are measures of a istributions ispersion. o&ever% each is compute ifferently anhas a ifferent interpretation. !he range is compute as the ifference bet&een the ma+imuman minimum values in a ataset. t represents the ispersion or sprea of the ata. !he

stanar eviation is base on the s$uare ifferences bet&een all ataset values an the meanof the ataset. n contrast to the range% the stanar eviation measures the ispersion of atavalues in relation to the mean or central location of a istribution. Another &ay to interpret thestanar eviation is a measure of the concentration of ataset values near the mean.


Difficulty: ,edium

Learning Objectie: !"#!4 E%&la

Chap003 Describing Data Numerical Measures

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Transcript of Chap003 Describing Data Numerical Measures