Q25 of 37 Page 14

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

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

Here, let A = 25 and h = 10



CLASS

MID - POINT(xi)

DEVIATION(di)


di = xi – 25

FREQUENCY(fi)

ui = di/h

fiui

0 - 10

5

- 20

7

- 2

- 14

10 - 20

15

- 10

10

- 1

- 10

20 - 30

25 = A

0

15

0

0

30 - 40

35

10

8

1

8

40 - 50

45

20

10

2

20

TOTAL

    

50

  

4

We have got


A = 25, h = 10, Σfi = 50 & Σfiui = 4


∵ mean is given by



⇒


⇒


Thus, mean is 25.8

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23

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.

 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
26

The mean of the following data is 42. Find the missing frequencies x and y if the Sum of frequencies is 100.[CBSE 2014]


Class interval

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

Frequency

7

10

x

13

y

10

14

9
27

The daily expenditure of 100 families are given below. Calculate f1 and f2 if the mean daily expenditure is Rs.188.[CBSE 2014]


Expenditure (in Rs.)

140 - 160

160 - 180

180 - 200

200 - 220

220 - 240

Number of families

5

25

f1

f2

5