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Question

Find the mean deviation about the median for the data

xi

15

21

27

30

35

fi

3

5

6

7

8

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Solution

The given observations are already in ascending order.

Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table.

xi

fi

c.f.

15

3

3

21

5

8

27

6

14

30

7

21

35

8

29

Here, N = 29, which is odd.

observation = 15th observation

This observation lies in the cumulative frequency 21, for which the corresponding observation is 30.

∴ Median = 30

The absolute values of the deviations from median, i.e.are

|xi – M|

15

9

3

0

5

fi

3

5

6

7

8

fi |xi – M|

45

45

18

0

40

∴


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