The two data sets below show the approximate number of gallons of gasoline Josie and Olivia put into their cars the last 10 times they filled their gas tanks. A dot plot titled josie's Gasoline (gallons). The number line goes from 8 to 12. There are 2 dots above 8, 2 above 9, 6 above 10, and 0 above 11 and 12. A dot plot titled Olivia's Gasoline (gallons). The number line goes from 8 to 12. There are 0 dots above 8 and 9, 6 above 10, 3 above 11, and 1 above 12.
Which measure of variability would most accurately compare the two data sets and why?
A) Range
B) Mean
C) Median
D) Standard Deviation

To compare the two data sets and determine the measure of variability that would be most accurate, we need to consider the characteristics of the data.

The dot plot for Josie's gasoline shows that the data points are more spread out, with 6 points above 10 and 0 points above 11 and 12. On the other hand, the dot plot for Olivia's gasoline shows a similar spread, with 6 points above 10, 3 points above 11, and 1 point above 12.

Based on the given information, we can see that both data sets have a similar range, as they both cover the same range from 8 to 12.

The mean is not an appropriate measure of variability in this case because it does not provide information about the spread or distribution of the data.

The median is also not the most accurate measure of variability because it only represents the middle value in the data set and does not take into account the spread or distribution of the data.

Therefore, the most accurate measure of variability to compare the two data sets would be the standard deviation. The standard deviation measures the average amount by which each data point in a set differs from the mean of the set. It provides a measure of how spread out the data points are from the mean. By calculating the standard deviation for both data sets, we can compare their variability more accurately.

Therefore, the correct answer is option D) Standard Deviation.