Final answer:
The measure of variation that quantifies how much data points differ from the mean is the standard deviation. Among the given data sets, b) {3, 4, 17, 52, 98} has the highest measure of variation due to the wide range and spread of its values.
Step-by-step explanation:
Measures of Variation
Measures of variation refer to statistical calculations that describe the spread or dispersion of data points in a dataset. One of the most common measures of variation is the standard deviation, which quantifies the amount by which each data point differs from the mean of the data set. Other measures of variation include range, variance, and interquartile range (IQR).
To determine which of the given data sets would have the highest measure of variation, we can look at the spread of the numbers. Here are the sets for reference:
a) {5, 10, 15, 20, 25}
b) {3, 4, 17, 52, 98}
c) {101, 102, 102, 103, 104}
d) {15, 15, 15, 15, 15}
Data set b) has data points that are spread out much more than the others, which indicates a higher measure of variation. This can be seen by the big difference between the smallest and largest values, as well as how spread out the numbers are from each other. Therefore, data set b) would have the highest measure of variation.