Question

each histogram represents a set of data with a median of 29.5. which set of data most likely has a mean that is closest to 29.5?

Explanation:

Step1: Recall the relationship between mean and median

In a symmetric distribution, the mean is equal to the median. When the distribution is skewed, the mean is pulled in the direction of the skew.

Step2: Analyze the histograms

The second histogram (the yellow - colored one) is more symmetric around the median value of \(29.5\). The first histogram (the orange - colored one) is less symmetric. A symmetric distribution implies that the mean is closer to the median.

Answer:

The set of data represented by the second (yellow - colored) histogram.