Question

The median of the following frequency distribution is 38. Find the value of a and b if the sum of frequences is 400 :

Class

10-20

20-30

30-40

40-50

50-60

60-70

70-80


Frequency

42

38

a

54

b

36

32

Answer 1

Step-by-step explanation:

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Answer 2

Given,

Median = 38

Frequency (N) = 400

To find,

Value of a and b

Solution,

Class frequency Cumulative f

10-20 42 42

20-30 38 80

30-40 a 80+a

40-50 54 134+a

50-60 y 134+a+b

60-70 36 170+a+b

70-80 32 202+a+b

Total frequency (f) = 400 (given)

400 = 202 + a + b

a+b = 198 (equation 1)

Here the median is 38

So the median class is 30-40

Therefore,

L = 30

N = 400

2 2

N = 200

Cf = 80

f' = a

h = 10

As per the formula,

Median = L + [N/2 - Cf] × h

Median = L + [N/2 - Cf] × h f

38 = 30 [200-80] × 10

a

38-30 = 120×10

a

a = 1200

8

a = 150

Now put the value of a in equation 1

We get,

a+b = 198

b = 198-150

b = 48

Therefore the value of a and b is 150 and 48 respectively.