Question

For the following data set, X: 9, 6, 8, 3, 8, 9, 3, 4, 3, 7:

Calculate:

1. Variance

2. Mode

3. Mean

4. Mean Average Deviation (MAD) about the mean

5. Median

Answer 1

Given values : 9 , 6 , 8 , 3 , 8 , 9 , 3 , 4 , 3 , 7

Number of observations = 10 = n (SAY)

Mean , = (9 + 6 + 8 + 3 + 8 + 9 + 3 + 4 + 3 + 7 ) / 10 = 6

Following table shows the calculations -

Given values (Xi)	(Xi - )	(Xi - )2
9	3	9
6	0	0
8	2	4
3	-3	9
8	2	4
9	3	9
3	-3	9
4	-2	4
3	-3	9
7	1	1
Total	0	58

Variance = ((Xi - ​​​​​​​)2) / n = 58/10 = 5.8

Mode of the data set is 3 (highest number of times it is repeated : 3 times)

Mean average deviation about the  Mean (MAD) = (Xi - ​​​​​​​) / n = 0

Arranging the data set in Ascending order -

3 , 3 , 3 , 4 , 6 , 7 , 8 , 8 , 9 , 9

Median is the centermost value = (5th + 6th) observation / 2 = (6 + 7) = 6.5

Therefore , all the answers -

• Answer 1 : Variance = 5.8
• Answer 2 : Mode = 3
• Answer 3 : Mean = 6
• Answer 4 : Mean deviation about the Mean = 0
• Answer 5 : Median = 6.5