which set of population data is the least dispersed from its mean?\n2, 3, 2, 9\n4, 0, 4, 0\n6, 2, 2, 2\n9…
which set of population data is the least dispersed from its mean?\n2, 3, 2, 9\n4, 0, 4, 0\n6, 2, 2, 2\n9, 3, 5, 3
Answer
Explanation:
Step1: Recall measure of dispersion
We can use the range as a simple measure of dispersion. The range is the difference between the maximum and minimum values in a data - set. Smaller range means less dispersion from the mean.
Step2: Calculate range for 2, 3, 2, 9
The maximum value is 9 and the minimum value is 2. Range = 9 - 2=7.
Step3: Calculate range for 4, 0, 4, 0
The maximum value is 4 and the minimum value is 0. Range = 4 - 0 = 4.
Step4: Calculate range for 6, 2, 2, 2
The maximum value is 6 and the minimum value is 2. Range = 6 - 2 = 4.
Step5: Calculate range for 9, 3, 5, 3
The maximum value is 9 and the minimum value is 3. Range = 9 - 3 = 6.
Step6: Compare ranges
The ranges are 7, 4, 4, 6. The smallest range is 4 for the data - sets 4, 0, 4, 0 and 6, 2, 2, 2. We can further calculate the variance or standard deviation for a more accurate comparison. But using the range, we note that for the set 4, 0, 4, 0, the values are more symmetrically distributed around the mean compared to 6, 2, 2, 2.