Question

the graph shows the ages of different concert - goers who have backstage passes. which statement is true about the graph? a late arrival who is 21 years old with a back - stage pass will make the mean greater than the median. the two holders of back - stage passes whose ages are above 40 make the mean age higher than the median age. the ages of concert - goers with backstage passes are skewed left, so the mean age is less than the median age. a concert - goer who is 18 years old and wins a back - stage pass will pull the mean more than 2 years less than the median.

Explanation:

Step1: Recall mean - median relationship in skewed data

The mean is affected by extreme values more than the median. In a right - skewed distribution, the mean is greater than the median; in a left - skewed distribution, the mean is less than the median.

Step2: Analyze the histogram

The histogram of the ages of concert - goers with backstage passes has a few high values (ages above 40) which are pulling the tail of the distribution to the right. This indicates a right - skewed distribution. The presence of these high values (outliers in the upper end) will increase the mean while having less of an impact on the median.

Step3: Evaluate each option

• Option A: A 21 - year - old is not an extreme value relative to the data set, so it won't make the mean greater than the median.
• Option B: The two holders of back - stage passes whose ages are above 40 are outliers on the high end. These outliers will increase the mean but have less of an impact on the median, making the mean age higher than the median age. This is correct.
• Option C: The data is skewed right, not left.
• Option D: An 18 - year - old is not an extreme value that would pull the mean more than 2 years less than the median.

Answer:

B. The two holders of back - stage passes whose ages are above 40 make the mean age higher than the median age.