Q23 of 37 Page 14

In an annual examination, marks (out of 90) obtained by students of Class X in mathematics are given below: [CBSE 2014]


Marks obtained

0 - 15

15 - 30

30 - 45

45 - 60

60 - 75

75 - 90

Number of students

2

4

5

20

9

10

Find the mean marks.

We will find the mean marks using step - deviation method, where A = Assumed mean and h = length of class interval.

Here, let A = 37.5 and h = 15



MARKS OBTAINED

MID - POINT(xi)

DEVIATION(di)


di = xi – 37.5

NUMBER OF STUDENTS(fi)

ui = di/h

fiui

0 - 15

7.5

- 30

2

- 2

- 4

15 - 30

22.5

- 15

4

- 1

- 4

30 - 45

37.5 = A

0

5

0

0

45 - 60

52.5

15

20

1

20

60 - 75

67.5

30

9

2

18

75 - 90

82.5

45

10

3

30

TOTAL

    

50

  

60

We have got


A = 37.5, h = 15, Σfi = 50 & Σfiui = 60


∵ mean is given by



⇒


⇒


Thus, mean marks are 55.5.

More from this chapter

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21

Find the mode of the following frequency distribution: [CBSE 2014]


Marks

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

Number of students

12

35

45

25

13
22

Heights of students of Class X are given in the following frequency distribution: [CBSE 2014]


Height (in cm)

150 - 155

155 - 160

160 - 165

165 - 170

170 - 175

Number of students

15

8

20

12

5

Find the modal height.


Also, find the mean height. Compare and interpret the two measures of central tendency.

 24

The following table gives the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method. [CBSE 2014]


Literacy rate (%)

45 - 55

55 - 65

65 - 75

75 - 85

85 - 95

Number of cities

4

11

12

9

4
25

Find the mean of the following frequency distribution using step - deviation method. [CBSE 2014]


Class

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

Frequency

7

10

15

8

10