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  • Find the mean deviation about the median of the following distribution: Marks Obtained 10 No. of students: 2

Find the mean deviation about the median of the following distribution:

Marks obtained 10 11 12 14 15
No. of Students 2 3 8 3 4

 

Answers (2)

The data distribution is given in the question.

We have to find the mean deviation about the median of the distribution in this question.

 Let us make a table of the given data and fill up the other columns after calculations

Marks obtained (x_{i})

Number of students  (f_{i})

Cumulative frequency

10

2

2

11

3

5

12

8

13

14

3

16

15

4

20

Total

20

 

Now here N=20 which is even.

Here, median  \\ M= \frac{1}{2} \left[ \left( \frac{N}{2} \right) ^{th}observation+ \left( \frac{N}{2}+1 \right) ^{th}~observation \right] ~~ \\

\\ ~ M=\frac{1}{2} \left[ \left( \frac{20}{2} \right) ^{th} observation+ \left( \frac{20}{2}+1 \right) ^{th}~observation~ \right] ~~ \\ \\ ~ M=\frac{1}{2}~ \left[ 10^{th}observation+11^{th}observation~ \right] ~~ \\

 Both these observations lie in cumulative frequency 13, for which corresponding observation is 12.

\\ M=\frac{1}{2} \left[ 12+12 \right] =12 \\

Posted by

infoexpert21

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Posted by

infoexpert21

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