Use the image to answer the question.

Question

Three dot plots labeled as A, B, and C each have a number line with arrows at both ends ranging from 5 to 12 in one-unit increments. Vertical columns of closed dots are plotted above certain numbers.

The median is the best measure of center for which data set?

data set C because the distribution is skewed
data set C because the distribution is skewed

data set B because the range is largest
data set B because the range is largest

data set B because the distribution is the flattest
data set B because the distribution is the flattest

data set A because the distribution is nearly symmetric

Answer 1

To determine which data set is best represented by the median as the measure of center, we need to consider the characteristics of each data set's distribution.

1. Data set C: If the distribution is skewed (either right or left), the mean can be heavily influenced by outliers, making the median a better measure of center.

2. Data set B: If the range is largest, that might indicate variability, but it does not necessarily inform us about the best measure of central tendency.

3. Data set B (again): The flatness of the distribution could indicate a uniform distribution, meaning that there are no significant outliers, and the mean could be a good representation of the center, but not necessarily.

4. Data set A: If the distribution is nearly symmetric, the mean and median would typically be similar, thus, the median is a reasonable measure of center, but not necessarily the best.

Given these points, the most appropriate answer is:

data set C because the distribution is skewed.

The median is often preferred over the mean as a measure of center when dealing with skewed distributions, as it is less affected by outliers or extreme values.