Question

Which data set is the most clustered around its mean?

a) 4, 10, 8, 6
b) 11, 3, 10, 4
c) 2, 9 ,13, 4
d) 11, 2, 9, 6

Answer 1

4, 10, 8, 6

Explanation:

Answer 2

Sample A

Explanation:

To find which is most clustered around mean, we can use either mean deviation or variance

Here let us use mean deviation

Mean deviation is calculated as sum of

|x-mean| for all x in the sample.

Sample a: Mean =7

Mean deviation = 3+3+1+1=8

Sample b: Mean = 7

Mean deviation = 4+4+3+3 =14

Sample c: Mean = 7

Mean deviation = 5+2+6+3 =16

Sample d: Mean = 7

Mean deviation = 4+5+2+1 =12

Thus we find that though mean is the same for all four samples mean deviation is the least for sample A

THus sample A is clustered around the mean