During 2005, 1,186,000 college-bound high school seniors took the ACT college admission test. The average score on

Question:

During 2005, 1,186,000 college-bound high school seniors took the ACT college admission test. The average score on the mathematics component was 20.7, with a standard deviation of 5.0. We are assuming that the math scores in data file XR03067 could have been the math scores for a sample of 400 college-bound seniors who took the ACT that year. (An important note: The mean and the standard deviation for our sample are close, but not exactly the same as the mean and standard deviation of the population from which the sample was obtained€”this is a key concept that is central to Chapter 8, Sampling Distributions.) Based on the assumed sample data in file XR03067,
a. Determine the mean, the median, and the standard deviation of the math scores in the sample.
b. Generate and interpret the box-and-whisker plot for the math scores in the sample.
c. What math score would a test-taker have to achieve to be higher than 75% of the sample members? To be higher than 25% of the sample members?
A computer and statistical software will be desirable and useful. However, any necessary calculations can also be done with the aid of a pocket calculator. For readers using statistical software, keep in mind the file-naming key€” for example, the data for Exercise 3.57 will be in data file XR03057.
In exercise