4 STAT

Saturday, April 22, 2023

AIRIL AHMAD


AIRIL AHMAD

STATISTICS

BYMR.AIRIL AHMAD

STATISTICS

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Pictograph

Bar graph

Line graph

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PIE CHARTA pie chart is a graphic representation of data using

sectors of a circle. The size of each sector shows the percentage of the overall data it represents.

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Example 1:Table shows the favourite fruit by students in 3 Harmoni

Name of fruits

Number of Students

Strawberry Apple Banana Grape

Sum of fruits that 3 Harmoni students like:

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Favourite Fruits

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Table shows the favourite fruit by students in 3 Harmoni

Name of fruit

Strawberry Apple Banana Grape

Number of Students

Sum of fruits that 3 Harmoni students like: 36

10 17 7 2

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CALCULATION

STRAWBERRY APPLE

GRAPE BANANA

036036

10 036036

170100

036036

2 0360

36

7 020070

0170

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How to draw the pie chart?`

1000

Strawberry

1700

Apple

700

Banana

200

Grape

00

100

200

300

400

500

600700 800 900

1000

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Example 2:Table shows the favourite games by students in 3 Amanah

Name of games

Number of Students

Baseball Basketball Bowling Golf

Total of games that 3 Amanah students like:

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Favourite Games

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Example 2:Table shows the favourite games by students in 3 Amanah

Name of games

Number of Students

Baseball Basketball Bowling Golf

Total of games that 3 Amanah students like: 20

8 7 3 2

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CALCULATION

Baseball Basketball

Golf Bowling

036020

8 036020

70144

036020

2 0360

20

3 036054

0126

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Example 3:

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EXERCISE - ORALLY

PAGE 71EX 4.1A1 , 2 , 3 , 4

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EXERCISE

PAGE 73EX 4.1B1 and 2 only

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EXERCISE - HOMEWORK

PAGE 75EX 4.1C1 and 2

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MODE

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WHAT IS MODE???

Mode is the most common factor or value, with the highest frequency in a set of data.

There are two methods to determine data mode:

a. Mode for a set datab. Mode for data from a frequency table

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Mode for a set data2 3 8 7 5 3 2 4 6 8

7 4 5 3 5 3 7 8 4 3

Solution:1.Rearrange the number from the smallest to the biggest

2 2 3 3 3 3 3 4 4 4 5 5 5 6 7 7 7 8 8 8

THEREFORE, 3 IS THE MODE because 3 appears mostly in the set of data

2. Find the most number appears in the set.

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Example 12 8 8 7 5 3 2 4 6 8

7 4 5 3 8 3 7 8 4 8

Solution:1.Rearrange the number from the smallest to the biggest

2 2 3 3 3 4 4 4 5 5 6 7 7 7 8 8 8 8 8 8

THEREFORE, 8 IS THE MODE because 8 appears mostly in the set of data

2. Find the most number appears in the set.

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Example 230 35 40 55 80 90

90 55 67 90 37 55

Find the mode for the given data

The most common number in the set of data above is……….

55

THEREFORE, 55 and 90 ARE THE MODES because 55 and 90 appear mostly in the set of data

90and

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Example 3

145 155 182 175 188 163Find the mode for the following data

There is no mode appear in this data.

THEREFORE,

AT TIMES THERE IS MORE THAN ONE MODE IN A SET OF DATA

OR

THERE IS NO MODE AT ALL

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number 1 2 3 4 5 6

frequency 5 1 4 6 1 3

A dice was thrown severals times and the numbers obtained was recorded as follows:

The most common number is………4

Therefore , 4 is the MODE

Mode for data from a frequency table

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Points 10 20 30 40

Number of students 6 13 24 7

The table below shows the points collected by a group of students in a game. Find the mode of the point.

The most common number is……… 30

Therefore , 30 is the MODE

Example 1

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WHAT IS MODE???

Mode is the most common fact or value, with the highest frequency in a set of data.

There are two methods to determine mode:– Mode for a set data– Mode for data from a frequency table

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Exercise

Page 80 Ex.4.2A Number 1 abcd Number 2ab (give answer only)


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MEDIAN

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MEDIAN = MIDDLE


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WHAT IS MEDIAN?

Median is the value in the middle of the set of data when the data is arranged in numerical order.

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ODD DATA

If the total number of data is odd, then the median is located in the middle of the set of data

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Example1 : Find the median of

10, 8, 7, 9, 6, 5, 7, 7,6

Rearrange

5, 6, 6, 7, 7, 7, 8, 9, 10

7

Median = 7

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EVEN DATA

If the total number of data is even, then the median is ‘average’ of the two middle values of the set of data

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Example 2 : Find the median of

10, 8, 8, 9, 6, 5, 7, 6, 6, 4

Rearrange

4 ,5, 6, 6, 6, 7, 8, 8, 9, 10

Median = (6+7) ÷ 2 = 13 ÷ 2 = 6.5

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ExerciseFind the median.

1. 12, 6, 3, 10, 2, 7, 6

Rearrange:

Median =

2. 42, 34, 68, 57, 83, 67,

49, 57, 45, 73

Rearrange:

Median =

3. 4kg, 8kg, 3kg, 8kg,7kg

Rearrange:

Median =

4. 18s, 11s, 9s, 16s, 20s, 11s, 19s, 13s

Rearrange:

Median =

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ExercisePg 85Ex. 4.2 C1 abcd & 2

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Number 1 2 3 4 5 6

frequency 5 1 4 3 1 3

a. Odd Data (example 1)

The median is………3

Median for data from a frequency table

176 10 1413 17

The middle position is at position 92

117

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Number of pen 1 2 3 4 5

frequency 4 3 8 2 6

a. Odd Data (example 2)

The median is………

Median for data from a frequency table

The middle position is at position

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Points 10 20 30 40


The median is……… 30

b. Even data (example 1)


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Mass (kg) 40 44 46 50


The median is……… 45

b. Even data (example 2)


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ExercisePage 85Ex.4.2cNumber 3 ab


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MEAN

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WHAT IS MEAN???

Mean is the average of a set of data.

Formula for mean:

Mean or = sum of all the values of the data total number of data

x

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Example 1:

Find the mean of 2 , 5 , 8 , 7 and 12

x Mean = 2 + 5 + 8 + 7 + 12

5

Mean = 34 = 6.8

5 x

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Example 2:In monthly test ,Ahmad obtains 86% for BM, 78% for BI, 90% for Mathematics and 76% for

Science. Calculate the mean of the data.

xMean = 86 + 78 + 90 + 76

4

Mean = 330 = 82.5

4 x

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Exercise:Find the mean:

1. 42, 34, 68, 57, 83, 67, 49, 57, 45

2. 4kg, 8kg, 3kg, 9kg, 7kg, 10kg

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ExercisePg.87Ex.4.2D1ab, 2

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ExercisePg.87Ex.4.2D1ab, 2 , 5ab, 6abc


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MEAN FROM THE FREQUENCY TABLE

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Number (n) 1 2 3 4 5 6

Frequency (f) 5 1 4 6 1 3

A dice was thrown several times and the numbers obtained was recorded as follows:

Mean= f x n = 66 = 3.3

f 20

Mean for data from a frequency table

f x n 5 2 12 24 5 18 66

20

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Number (n) 1 2 3 4 5 6

Frequency (f) 6 2 1 5 4 3

Mean= f x n = 71 = 3.38

f 21

f x n 6 4 3 20 20 18 66

21

Example 2

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Points 10 20 30 40


The table below shows the points collected by a group of students in a game. Find the mode of the point.

Example 1

50

f x n 60 260 720 280 1320

Mean= f x n = 1320 = 26.4

f 50

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ExercisePage 87Ex.4.2DNumber 3ab & 4


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MEAN PROBLEM SOLVING

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Example 1 Given the mean of a set of data 2, 4, 5, 8, x,

12 is 7. Find the value of x.

2 + 4 + 5 + 8 + x + 12 = mean

6 x + 31 = 7

6

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x + 31 = 7 x 6

x + 31 = 42

x = 42 - 31

x = 11

x + 31 = 7

6

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Example 2 Given the mean of a set of data 1, 2, 4, x + 3,

7, x, 8, 9 is 5. Find the value of x.

1+ 2+ 4+ x + 3+ 7+ x + 8+ 9 = mean

8

2x + 34 = 5

8

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2x + 34 = 5 x 8 2x + 34 = 40

2x = 40 - 34

2x = 6 x = 6

2

x = 3

2x + 34 = 5

8

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1. The mean of 6, 8, x, 15, 18 and 27 is 14. Find the value of x.

2. The mean of 10, 15, 20, x, 30, 40 and 48 is 28. Find the value of x.

3. The mean of 8, 12, x, 19, 24 and 30 is 18. Find the value of x.

4. The mean of 4, x, 5, 8 and 9 is 6.4. Find the value of x.

Exercise

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