Question

the histogram represents the distributions of essay scores for high school sophomores and juniors in a contest. which statements are true about the data used to create the histogram? select three options. the mean is the best comparison of the measures of center. the juniors tended to have higher essay scores than the sophomores. the medians of both data sets are equal. the interquartile range is the best comparison of the measure of variability. a histogram is the best way to show that both distributions are nearly symmetric.

Explanation:

Step1: Analyze the mean as a measure of center

Since the data has outliers (the small bars at the extremes), the median is a better measure of center than the mean. So the statement "The mean is the best comparison of the measures of center" is false.

Step2: Compare junior and sophomore scores

Looking at the histogram, for most score values (e.g., score = 3, score = 4, score = 6), the number of juniors (blue bars) is higher than or equal to the number of sophomores (yellow bars). So "The juniors tended to have higher essay scores than the sophomores" is true.

Step3: Check the medians

To find the median, we need to order the data. But from the histogram, we can see that the distributions are not the same. The medians are not equal.

Step4: Analyze the inter - quartile range (IQR) as a measure of variability

Since the data has outliers, the IQR (which is less affected by outliers) is a better measure of variability than the range. So "The interquartile range is the best comparison of the measure of variability" is true.

Step5: Check the symmetry of the histogram

The histograms are not nearly symmetric. There are small bars (outliers) and the distributions are skewed in different ways. So "A histogram is the best way to show that both distributions are nearly symmetric" is false.

Answer:

The juniors tended to have higher essay scores than the sophomores; The interquartile range is the best comparison of the measure of variability.