Statistics Initial Presentation(Handout)

7/24/2019 Statistics Initial Presentation(Handout)

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Measures of CentralTendency

Mean,Median and Mode

for Ungrouped Data

Basic Statistics

By: Noshielta Castillo

Rizza Maalac

Jaycon Malicdem


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Measures of CentralTendency

In laymans term, ameasure of central tendencyis an AVERAGE. It is a singlenumber of value which canbe considered typical in a set

of data as a whole.

or e!ample, in a class of"# students, the averageheight would be the typicalheight of the members of this

class as a whole.

Measures of central tendency are set of data by

identifying the central position within the set of

data and are numerical descriptive measures

which indicate or locate the center of a

distribution or data set.


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MEAN

Among the three measures of centraltendency, the mean is the most popular and

widely used. $he mean is e%ual to the sum of allthe values in the data set divided by the numberof values in the data set it is sometimes called thearithmetic mean.

If we compute the mean of the population, wecall it the parametric or population mean, denotedby (read mu).

If we get the mean of the sample, we call it thesample mean and it is denoted by (read x bar).

$he MEANof a set of values or measurements isthe sum of all the measurements divided by thenumber of measurements in the set.


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Mean for Ungrouped Data

Example 1:

&s. 'ulit collects the data on the ages of &athematicsteachers in 'anta Rosa 'chool, and her study yields thefollowing(

)* )+ * )- )+ ))"#

Solution:

= 35

Based on the computed mean, 38 is the average age of

Mathematics teachers in SRS.

For ungrouped or raw data, the mean has the following

formula.

where = mean

= sum of the measurements or values

n = number of measurements


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Your turn!

Mang John is a meat vendor. The following are his sales forthe past six days. Compute his daily mean sales.

Tuesday P !""#ednesday ! $""Thursday $ ""Friday % &""

'aturday () ""'unday (& %""

'olution*

= (, (""

The average daily sales of Mang John is P(,("".


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Example

-elow are maya/s sub0ets and the orresponding number

of units and grades she got for the previous grading

period. Compute her grade point average.

Subject Units rade

Filipino .1 !$

2nglish (. !

Mathematis (. !!

'iene (.! !3

'oial 'tudies .1 !$

T42 (.) !&

MP25 (.) !3

= !$.(

maya/s average grade is !$.(


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Your turn!

James obtained the following grades in his five sub0ets forthe seond grading period. Compute his grade point average.

'olution*

= !3.$3

James general average is !3.$3

Subject Units rade

Math (. 1"

2nglish (. !$

'iene (.! !!

Filipino ".1 !3

M6-78 (. !3


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ier"type #uestion

e!t are e!amples of /i0ert1type statements.

Respondents will choose the number which bestrepresents their feeling regarding the statements.ote that the statements are grouped accordingto a theme.

This is used if the researher wants to 9now the feelings oropinions of the respondents regarding any topi or issues of

interest.

!hoices

:'; 'trongly gree% :; gree

& :8; 8eutral

) :


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Students" persona# confidence in #earningStatistics

5 $ 3 % &

(. am sure that an learn 'tatistis

). thin9 an handle diffiult lessons in'tatistis.

&. an get good grades in 'tatistis.

Source: B.E. Blay, Elementary Statistics

-elow are the responses in the 4i9ert+type ofstatements above. The table below shows the meanresponses and their interpretation. >sing the formula foromputing the weighted mean, he9 the orretness of thegiven means on the table.

5 $ 3 % & Mean 'nterpretation

( &$ ( (! " ( %.(% gree

) (! %% &3 ! ( &.$ gree

& (! %! )! " ( &.!$ gree


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ie"type Mean$nterpretation

(." + (.31 + 'trongly


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Your turn!-elow is the result of the responses to the following 4i9ert+type statements . 'olve for the mean and give the

interpretation.

5 $ 3 % & Mean 'nterpretation

( && %1 )$ ( (

) & % &( " (

& &% ! )( " "

Students" perception on Statistics as asubject

5 $ 3 % &

(. thin9 'tatistis is a worthwhile, neessary

sub0et

). will use 'tatistis in many ways as aprofessional

&. /ll need a good understanding of 'tatistisfor my researh wor9


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%roperties of Mean

(. Mean an be alulated for any set of

numerial data, so it always exists.

). set of numerial data has one and only one

mean.

&. Mean is the most reliable measure of entraltendeny sine it ta9es into aount every item

in the set of data.

%. t is greatly affeted by extreme or deviant

values :outliers;

. t is used only if the data are interval or ratio.


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MED$AN

$he MED$AN& denoted &d, 2lace the value

order and 3nd the middle number or the mean of

the two middle numbers.

($ (3 (! (1 )" )( ))

Median

($ (3 (! (1 )" )( )) )&

Median


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Your turn!

Compute the median and interpret the result.(. n a survey of small businesses in Tondo, (" ba9eries

report the following numbers of employees*(, (%, (), (1, (&, (% (, (!, (&, (1.

). The random savings of )ndyear high shool studentsreveal the following urrent balanes in their ban9

aounts*

&. The following are the lifetimes of 1 lightbulbs in

thousands of hours.

'tudents - C < 2 F ? 5

Current -alanes P&%" &" %" "" &$" 3$" !"" 3%"

4ightbulb - C < 2 F ? 5

4ifetime (.( (.( (.) (.( (.% .1 .) (.) (.3


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%roperties of Median

(. Median is the sore or lass in the distributionwherein "@ of the sore fall below it and

another "@ lie.

). Median is not affeted by extreme or deviant

values.

&. Median is appropriate to use when there are

extreme or deviant values.

%. Median is used when the data are ordinal.

. Median exists in both Auantitative or Aualitative

data.


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M'DE

$he M'DE& denoted &o&4r modal value, place

the numbers in value order then count on how many

of each number.

2xamples*

Find the Mode.

(. The ages of five students are* (3, (!, )&, )", and (1

). The following are the desriptive evaluations of

teahers* B', ', B', B',

&. The grades of five students are * %.", &., %.", &., and

(."%. The weights of five boys in pounds are* ((3, )(!, )&&,

()", and ((3


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%roperties

(. t is used when you want to find the valuewhih ours most often.

). t is a Aui9 approximation of the average.

&. t is an inspetion average.

%. t is the most unreliable among the three

measures of entral tendeny beause its

value is undefined in some observations.


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Your turn!

(ind the mode and interpret it.

(. The following table shows the freAueny of errorsommitted by (" typists per minute.

). random sample of ! mango trees reveals thefollowing number of fruits they yield

&. The following are the sores of 1 students in aMathematis AuiD.* (), (, (), !, 3, (, (1, )%, (&

Mango Tree - C < 2 F ? 5

8o. of fruits !" 3" !" 1" !) !) 1" !)

Typists - C < 2 F ? 5 J

8o. of errors per min. & & 3 ) ! ! % 3 ("


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(eferrences)

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