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Question

Find the mean, mode and median of the following frequency distribution. [CBSE 2010]

Class 0−10 10−20 20−30 30−40 40−50 50−60 60−70
Frequency 4 4 7 10 12 8 5

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Solution

To find the mean let us put the data in the table given below:
Class Frequency (fi) Class mark (xi) fixi
0−10 4 5 20
10−20 4 15 60
20−30 7 25 175
30−40 10 35 350
40−50 12 45 540
50−60 8 55 440
60−70 5 65 325
Total fi = 50 fixi = 1910

Mean=ifixiifi =191050 =38.2

Thus, mean of the given data is 38.2.

Now, to find the median let us put the data in the table given below:
Class Frequency (fi) Cumulative frequency (cf)
0−10 4 4
10−20 4 8
20−30 7 15
30−40 10 25
40−50 12 37
50−60 8 45
60−70 5 50
Total N = ∑fi = 50

Now, N = 50 N2=25.

The cumulative frequency just greater than 25 is 37, and the corresponding class is 40−50.

Thus, the median class is 40−50.

∴ l = 40, h = 10, N = 50, f = 12 and cf = 25.


Now,

Median=l+N2-cff×h =40+25-2512×10 =40

Thus, the median is 40.

We know that,
Mode = 3(median) − 2(mean)
= 3 × 40 − 2 × 38.2
= 120 − 76.4
= 43.6

Hence, Mean = 38.2, Median = 40 and Mode = 43.6

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