Question

Determine whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If​ so, what is​ it?

Answer 1

Answer:

It seems the question is incomplete as the two data sets implied from the question are not visible.

However, two data sets having identical measures of center have a difference.

Step-by-step explanation:

Let's consider these two data sets:

2, 2, 3, 5, 6, 6 and 1, 1, 1, 1, 1, 19

Both were contrived.

The most reliable among the measures of center is the mean. The mean of each is calculated by summing the data and dividing by the number of elements. In both sets, the mean is 4.

The data in the first set seem to be concentrated around the mean indeed. But for the second data set, one of them, 19, is obviously very far from the others and the mean. We need another measure to describe this: standard deviation.

Its formula is:

$\rho=\sqrt{\dfrac{\sum (x-\overline{x})^2}{n}}$

$x$ represents each data, $\overline{x}$ is the mean and $n$ is the number of items. $x-\overline{x}$ is the deviation from the mean of each data item.

For the first data set, $\rho=\sqrt{6}=2.45$

For the second data set,

$\rho=\sqrt{45}=6.71$

The low value of $\rho$ for the first set indicates that the items are all closer to the mean than for the second set.

Variance is the square of the standard deviation. It could also be used.