The test grades for a certain class were entered into a Minitab worksheet, and then Descriptive Statistics were requested. The results were: MTB> Describe ‘Grades’. N MEAN MEDIAN TRMEAN STDEV SEMEAN Grades 28 74.71 76.00 75.50 12.61 2.38 MIN MAX Q1 Q3 Grades 35.00 94.00 68.00 84.00
You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60, … but you don’t know what the other individual grades are. Nevertheless, a knowledgeable user of statistics can tell a lot about the data set simply by studying the set of descriptive statistics above.
a. Write a description of what the results in the box tell you about the distribution of grades. Be sure to address the general shape of the distribution, any unusual features, including possible outliers, the location of the middle 50% of the data and any significance in the difference between the mean and the median.
b. Construct a boxplot for the test grades