Question

A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows:

First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0

Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3

Which is the best measure of center for third period and why? (5 points)

a
Interquartile range, because there is 1 outlier that affects the center

b
Standard deviation, because there are no outliers that affect the center

c
Mean, because there are no outliers that affect the center

d
Median, because there is 1 outlier that affects the center

Answer 1

The best measure of center for the third period in this case is the median (option d).

The median is less sensitive to extreme values (outliers) compared to the mean. Looking at the data set for the third period, there is one outlier with a value of 8. The median is not influenced by extreme values, so it provides a more robust measure of center in the presence of outliers.

Options a and b are incorrect because the interquartile range and standard deviation, respectively, are measures of spread or dispersion, not center. Option c is incorrect because the mean is sensitive to outliers and can be skewed by extreme values, making it less appropriate when there are outliers in the data.