Question

a school district wanted to compare act scores between two of its schools (school a and school b). the dotplots below summarize the act scores for simple random samples of 30 students from each school. the median score was 22 for both samples. which of the following statements is true about the mean act for each sample?
o the mean score for the sample from school a is equal to the mean score for the sample from school b.
o the mean score for the sample from school a is less than the mean score for the sample from school b.
o the mean score for the sample from school a is greater than the mean score for the sample from school b.
o we cannot determine the relationship between the mean act scores without knowing the actual scores on the exam.

Explanation:

Step1: Analyze the dotplots' skewness

School A's dotplot has more data points on the right (higher scores) and some low - tail outliers, but the main cluster is around the median. School B's dotplot is more symmetric around the median, but when we look at the distribution of scores: School A has a number of relatively high - scoring points (the right - hand dots) and School B has more points in the lower - middle range.

To understand the mean, we know that the mean is affected by the values of all data points. For School A, even though there are some low - scoring outliers, the presence of a significant number of high - scoring points (compared to School B's distribution) will pull the mean up. School B's distribution is more concentrated in the middle - lower part relative to School A's high - end points.

Step2: Compare the means

The median is the same for both, but the mean is sensitive to extreme values (both high and low). In School A, the data has a right - skewed tendency (more high - value points) compared to School B. When we calculate the mean, the higher - valued data points in School A will increase its mean. School B's data is more evenly distributed around the median but without the same number of high - end points as School A. So, the mean of School A's sample will be greater than the mean of School B's sample.

Answer:

The mean score for the sample from school A is greater than the mean score for the sample from school B.