Number of goals scored in one season at Whitmore College soccer games follows:

Question

0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4

Which measure of variability—IQR or MAD— best describes the spread of the dataset?

(1 point)
Responses

MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical

IQR; the data distribution is skewed
IQR; the data distribution is skewed

MAD; the data distribution has outliers
MAD; the data distribution has outliers

IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical

Answer 1

IQR; the data distribution is skewed

Answer 2

Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points

Answer 3

The mean is the measure of center that is most affected by outliers. This is because the mean is calculated by taking the sum of all the data points and dividing by the total number of data points, so even one outlier can significantly affect the calculation of the mean.

For example, consider the following set of data with 10 data points:

10, 12, 14, 15, 16, 18, 20, 22, 24, 500

The median of this data set is 17, which is not significantly affected by the outlier value of 500. The mode is not applicable as there are no repeated values.

However, the mean of this data set is calculated as:

(10 + 12 + 14 + 15 + 16 + 18 + 20 + 22 + 24 + 500) ÷ 10 = 61.9

As we can see, the presence of the outlier value of 500 has significantly skewed the value of the mean.