4. The five-number summary below shows the grade distribution of a STAT 200 quiz

Question

4. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 500 students. 20 45 65 75 100 0 10 20 30 40 50 60 70 80 90 100 Answer each question based on the given information, and explain your answer in each case. (a) What is the minimum in the grade distribution? (b) Which quarter has the smallest spread of data? What is that spread? (c) Find the interquartile range (IQR) in the grade distribution. (d) Are there more students in the score band of 20 - 40 or 60 - 80? Why? (e) Can the average score be determined based on the given information? Why or why not?

Explanation / Answer

a) Minimum value = 20

b) The 3rd quarter has the smallest spread of data because the distance between median and 3rd quartile is the least.

Spread = 75 - 65 = 10

c) IQR = Q3 - Q1 = 75 - 45 = 30

d) There seems to be more students in 60 - 80 score band because it covers more than 25% of the area.

e) No, the average score can't be determined because we don't have the individual scores to determine the sum of those scores and without the sum, we can't find the average score. If the boxplot would have been perfectly symmetric then the mean would have been equal to the median and only in that case, we can determine the average score.

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