Q18 of 37 Page 14

Find the mean of the following frequency distribution using a suitable method: 

[CBSE 2013]


Class

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

Frequency

25

40

42

33

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 = 45 and h = 10



CLASS

MID - POINT(xi)

DEVIATION(di)


di = xi – 45

FREQUENCY(fi)

ui = di/h

fiui

20 - 30

25

- 20

25

- 2

- 50

30 - 40

35

- 10

40

- 1

- 40

40 - 50

45 = A

0

42

0

0

50 - 60

55

10

33

1

33

60 - 70

65

20

10

2

20

TOTAL

    

150

  

- 37

We have got


A = 45, h = 10, Σfi = 150 & Σfiui = - 37


∵ mean is given by



⇒


⇒


Thus, mean is 42.53.

More from this chapter

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16

Find the mean of the following data, using step - deviation method: [CBSE 2013]


Class

5 - 15

15 - 25

25 - 35

35 - 45

45 - 55

55 - 65

65 - 75

Frequency

6

10

16

15

24

8

7
17

The weights of tea in 70 packets are shown in the following table: [CBSE 2013]


Weight (in grams)

200 - 201

201 - 202

202 - 203

203 - 204

204 - 205

205 - 206

Number of packets

13

27

18

10

1

1

Find the mean weight of packets using step - deviation method.

 19

The median of the following data is 16. Find the missing frequencies a and b if the Total of frequencies is 70. [CBSE 2013]


Class

0 - 5

5 - 10

10 - 15

15 - 20

20 - 25

25 - 30

30 - 35

35 - 40

Frequency

12

A

12

15

b

6

6

4
20

Compute the mode of the following data: [CBSE 2013]


Class

0 - 20

20 - 40

40 - 60

60 - 80

80 - 100

Frequency

25

16

28

20

5