which set of population data is the least dispersed from its mean?\no 2,3,2,9\no 4,0,4,0\no 6,2,2,2\no 9,3,5,3

Answer:

4, 0, 4, 0

Explanation:

Step1: Recall measure of dispersion

We can use the range as a simple measure of dispersion. The smaller the range, the less dispersed the data is from the mean.

Step2: Calculate range for 2, 3, 2, 9

Range = 9 - 2 = 7

Step3: Calculate range for 4, 0, 4, 0

Range = 4 - 0 = 4

Step4: Calculate range for 6, 2, 2, 2

Range = 6 - 2 = 4

Step5: Calculate range for 9, 3, 5, 3

Range = 9 - 3 = 6

Step6: Compare ranges

The sets 4, 0, 4, 0 and 6, 2, 2, 2 have the smallest range among them. But if we consider the mean - for 4, 0, 4, 0, mean $\bar{x}=\frac{4 + 0+4 + 0}{4}=2$ and the values are closer to the mean compared to 6, 2, 2, 2 where mean $\bar{x}=\frac{6 + 2+2 + 2}{4}=3$. So the set 4, 0, 4, 0 is the least dispersed from its mean.