Question

Calculate mean deviation about median for the items. 7 4 10 9 15 12 7 9 7​

Answer 1

Step-by-step explanation:

Arrange data in ascending order,

2,3,4,6,9,10,13

No. of observation n=7(odd)

Median=n+1/2 =4th observation

Hence median =6

Now we calculate mean deviation about median, i.e;

⟹ ∑∣xii−M∣/7 =

∣2−6∣+∣3−6∣+∣4−6∣+∣6−6∣+∣9−6∣+∣10−6∣+∣13−6∣/7

23/7=3.28

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Answer 2

The main deviation about median for the given data would be 2.33

Given

• 7, 4, 10, 9 ,15, 12 ,7 ,9 ,7

To find

• mean deviation about median

solution

we are provided with raw data and are asked to estimate the main deviation about median for the given data.

previous knowledge

Mean deviation about mean for this type of data is given by the equation,

1/n Σ|x-A|

where A is the median of the distribution.

7, 4, 10, 9 ,15, 12 ,7 ,9 ,7

arranging in ascending order,

4,7, 7, 7, 9, 9, 10, 12, 15.

n = 9 (odd)

median = (n+1)/2 observation

or, (9+1)/2 = 10/2 = 5th observation

or, median = 9

deviation from mean for each observation

|4-9| = 5

|7-9| =2

|7-9| =2

|7-9| =2

|9-9| = 0

|9-9| = 0

|10-9| = 1

|12- 9| = 3

|15-9| = 6

thus, Σ|x-A| = 21

main deviation about a median would,

1/9 (21)

or, 2.33

Therefore, the main deviation about median for the given data would be 2.33

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