Chapter13 Statistics

8/16/2019 Chapter13 Statistics

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Chapter 13

Math

Form 2

13.1 Data

13.2 Frequency

13.3 Representing and InterpretingData to Solve Problems



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• Statistics is the science of collecting,organising, interpreting and analysing data.

• Two types of data:(i) Data obtained by counting(ii) Data obtained by measuring

• Frequency of a particular data refers to the

number of times the data appears in astatistics.• frequency table contains the rele!ant and

the frequency of each data.

S t a t i s t i c sS t a t i s t i c s



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13.1 Data• 13.1A Classifying Data

• 13.1B Collecting and Recording Data



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"#." $lassifying Data"#." $lassifying Data

• Data is a collection of information or facts on a matter

• Numerical data are data that involves numbers

• There are two tyes of numerical number 1. data obtained from counting

!. data obtained from measuring

$ollecting data by

measuring needs tools

or apparatus li%e rulers,balances, stopwatches

and thermometers



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"#."& $ollecting and 'ecording Data"#."& $ollecting and 'ecording Data• "hen collecting data# we have to determine whether the data can be collected

by counting or measuring .

• Collect the data using the correct method .

• The data collected needs to be arranged and recorded systematically# normallyin a table.

n a classroom, #

students are as%ed

about their hobbies. The

results are: "* students

li%e reading, # students

li%e di!ing, * students

li%e +ogging, studentsli%e camping, - students

li%e playing %ite and "

student li%e singing.

obbies/umber ofstudents

'eading "*

Di!ing #

0ogging *

$amping

1laying %ite -

Singing

"5

http://www.smileycentral.com/?partner=ZSzeb001



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Determine whether the following data is collected byDetermine whether the following data is collected by

counting or measuring.counting or measuring.

Data 2ethod

") The number of students in2alaysia.

) The number of boo%s in thelibrary.

#) The daily temperaturesin a town in a wee%.

*) The number of maga3inessold in a day.

4) The !olume of water in a tan%.

-) The weight of each student in a group.

counting

counting

measuring

counting

measuring

measuring




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• 13.!A Determining the $re%uency of Data

•13.!B Constructing Tally Charts and $re%uency Tables

• 13.!C &btaining 'nformation from $re%uency Tables

13.2 Frequency

2ar%s Frequency

5 4

6 "-

7 5

"

Frequency

887

8888 88886

88885

8888 8-

88884

TallyScore

2ar%s 5 6 7 "

Frequency 4 "- 5



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13.2A Determining the Frequency of Data

Frequency is the number of times a

particular data appears in a set of data.The following data shows the group of

numbers.

",

"#,

",

"",

"#,

"",

"*,

"",

",

",

"#,

",

"#,

"",

"*,

",

",

"*,

"*,

"",

"#,

"#,

"",

",

"*.

tate the frequency of each

number.

Solution:

Frequency of "" 9Frequency of " 9

Frequency of "# 9

Frequency of "* 9

-6

-

4

The highestfrequency is "

and the lowest

frequency is "*.



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Frequency

7

6

5 -

4

TallyScore

13.2! "onstructing Tally "harts and Frequency Tables.

The following data shows the

scores of students in a

#athematics test. "onstruct

a tally chart and state the

frequency for each score.

tally chart can be performed as follows

a) 2ar% a slash for a particular information e!ery time it

appears in the set of data.b) $ross the other four slashes ( 8888 ) for e!ery fifth time an

information appears.

c) $ount the number of slashes and write down the

frequency for each information. The counting is made

easier as the data is grouped in fi!es.

5

6

-

4

6

6

4

5

-

4

6

4

7

5

4

-

6

6

-

5

6

6

-

-

7

4

-*

"

8888

8888 8 8888

8888 8888

88 9





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13.2! "onstructing Tally "harts and Frequency Tables.a) frequency table is a table that shows a set of data and their

respecti!e frequency.

b) frequency table can be performed hori3ontally or !ertically.

hori3ontal frequency table has two rows whereas a !ertical

frequency has two columns.

2ar%s 5 6 7 "

Frequency 4 "- 5

2ar%s Frequency

5 4

6 "-

7 5

"

ori3ontally Frequency table

ertically Frequency table



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13.2" $btaining %nformation from Frequency Tables.

;<ample:

The table shows the mar%s obtained by the Form ;lite

students in a mathematics test. Study the table and answerthe questions below that follow.

2ar%s " # * 4 - 5 6 7 "

Frequency " * "" 5 7

a) ow many students are there in

the Form ;lite=

b) f the passing mar% is 4, how

many students failed in the test=

c) f a student scores 6 or abo!e,

she is considered scored . >hat

is the percentage of students that

scored =

* students

4 students

"6 < " 9 *4?

*



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"#.# 'epresenting and nterpreting Data to Sol!e 1roblems"#.# 'epresenting and nterpreting Data to Sol!e 1roblems

• 13.3 A (ictograms

• 13.! B Bar Charts

• 13.!C )ine *rah

@ear /umber of houses

was sold out

"

#

Aey: represent " houses



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"#.# 1ictograms"#.# 1ictograms

#a) $onstructing 1ictograms

i. 1ictograms use symbols or pictures to represent a set of

data. The frequency of a data is represented by the number

of symbols or pictures used.

ii. Data represented in a pictogram will be attracti!e and easy

to understand as well as to remember.iii. pictogram can be constructed hori3ontally or !ertically.

i!. To construct a pictogram, follow the steps below:

Step " : Decide on a suitable symbol to represent the data.

Step : Decide the frequency represented by one symbol.

Step # : 1repare the table and draw a suitable number ofsymbols for e!ery data according to the frequency

gi!en. The symbols must be drawn uniformly.

Step * : >rite the title and the %ey (or legend) for the

pictogram

;<ample:

Fruits /umber of students

orange

mango

apple



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The table below shows the number of bicycles

sold by a shop in a certain month.

2onth /umber of bicycles

pril

2ay

0une

0uly

'epresents 4 bicycles

2onth pril 2ay 0un 0uly

/umber of bicycle "4 #4 #

Step ". symbol of

bicycle is suitable

to be used.

Step . >e use one

symbol to

represent 4

bicycles.

Step #. >e can

then construct a

hori3ontal or

!ertical pictogram.


/umber ofbicycle

erticalpictogram

ori3ontal pictogram



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"#.#& &ar $harts"#.#& &ar $harts

#a) $onstructing &ar $hartsi. &ar charts use !ertical or hori3ontal bars to represent data.

ii. The bar are rectangles of equal width. The height or length

of a bar is proportional to the frequency.

iii. To construct a bar chart, follow the steps below:

Step " : $hoose a suitable scale. Step : Determine the length of each bar according to the

frequency and the selected scale.

Step # : Draw the bars !ertically or hori3ontally. 2a%e sure

the bars are of equal width. >rite the title and %ey to

the chart.

Step * : $hec% all information on the bar chart with the

information gi!en in the frequency table.;<ample:



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The following table below shows the number of

members of 2athematics Society in a school.

$onstruct a bar chart to represent the data.

Form/umber ofmembers

Bne *

Two -

Three "

Four "

Fi!e 7

Step ". Since the

number of membersis large (* t "),

use the scale ": or "

square represent

members.

Form "

/ u m b e r o f S t u d e n t s

*

-

6

"

2embers of 2athematics Society

"

"*

Form Form # Form * Form 4

Step . The length of

each bar is as follows:

* membersC squares- membersC # squares

" membersC-squares

" membersC4 squares

7 membersC*squares



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"#.#& Double !ertical &ar $harts"#.#& Double !ertical &ar $hartsThe following table below shows the number of members of babies born

in a hospital in four month. $onstruct a bar chart to represent the data.


/umber ofbabies

&oys "Eirls "6

&oys *Eirls "4

&oys "4Eirls "4

&oys 7Eirls "

#

-7

"

"4

"6

"

*

/ u m b e r o f b a b i e s

pril

/umber of babies born

2ay 0une 0uly

&oy

Eirl

2onth



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"#.#& Double ori3ontal &ar $harts"#.#& Double ori3ontal &ar $hartsThe following table below shows the number of members of babies born

in a hospital in four month. $onstruct a bar chart to represent the data.2onth pril 2ay 0un 0uly

/umber ofbabies

&oys "Eirls "6

&oys "4Eirls "

&oys "6Eirls "4

&oys 7Eirls "

# - 7 " "4 "6 " *

/umber of

babies

pril

/umber of babies born

2ay

0une

0uly

&oy

Eirl

2onth

5 # ##



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"#.#$ ine Eraphs"#.#$ ine Eraphs

;<ample:

#a) $onstructing ine Eraphs

i. line graph is used to to represent data obtained o!er a

period of time. s such the hori3ontal a<is in a line graphalways represents a period of time (years, months, wee%s,

days and hours).

ii. To construct a line graph, follow the steps below:

Step " : $hoose an appropriate scale.

Step : Draw the two a<is and plot the points representingthe data.

Step # : 0oin all the points with straight lines.

Step * : Ei!e a suitable title to the line graph.



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The following table below shows the number of students in!ol!ed in

uniformed organisations in a school. $onstruct a line graph to

represent the data.

"#.#$ $onstructing ine Eraph."#.#$ $onstructing ine Eraph.

"777

/ u m b e r o f S t u d e n

t s

4

""4

4

@ear

#

#4

" #

@ear "777 " #

/umber of students "4 # "54 #4

Step " : $hoose an

appropriate scale.

Step : Draw the twoa<is and plot the

points representing

the data.

Step # : 0oin all the

points with straightlines.

Step * : Ei!e a

suitable title to the

line graph.

20



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"#.#D 1roblemCSol!ing"#.#D 1roblemCSol!ingnformation from pictograms, bar charts and line graphs are

used to sol!e problems in statistics.

Frequency

7

6 5

-

4

TallyScore

8888

8888 8

8888 888

88Solution:

") The table below shows a tally chart ofthe mar%s obtained by a group of

students in a test. State the percentage

of students who obtained more than 5 mar%s.

-

4#*

9 # G * < "

9 5 < "

9 #4?



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"#.#D 1roblemCSol!ing"#.#D 1roblemCSol!ing

Solution:

) The table below shows the score obtained by a shooter

in shooting company. State the score with the highest

frequency.

Frequency of " 9

Frequency of 9Frequency of # 9

Frequency of * 9

Frequency of 4 9

" 4 # * 4

# # " 4

* " " 4 # *

4 * "

4

5*

#

4

The highest frequency is



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Solution:

#) The pictogram below shows the number of tourists who

!isited Tasi% Aenyir in four consecuti!e days. State thenumber of tourists who !isited Tasi% Aenyir on Friday

and Saturday.

9 (7 G -) <

9 "4 <

9 #

Day /umber of !isitors

>ednesday

Thursday

Friday

Saturday

'epresents tourists



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Solution:

*) The bar chart below shows the number of waiters and

waitresses in three hotels. State the difference between

the number of waiters and the number of waitresses.

. o t e l

1

H

'

/umber of waiters8waitresses* 6 " "- * 6 # #-

>aiter >aitress

9 (" C 7) < *

9 # < *

9 "



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Solution:

4) The line chart below shows the profit made by a

company

fi!e consecuti!e days. Find the a!erage of the profit.

1 r o f i t ( ' 2

)

Day

9 " G G "4 G 4 G #

4

9 "

4

9 '2

2 o n d a y

T u e s d a y

>

e d n e s d a y

T h u r s d a y

F r i d a y

4

"

"4

4

#



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Chapter13 Statistics

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