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 maximum in the grade distribution? (b) Which quarter has the smallest spread of data? What is that spread? (c) Find the range in the grade distribution. (d) Are there more students in the score band of 45- 65 or 65 - 852 Why? (e) Can the average score be determined based on the given information? Why or why not?

Explanation / Answer

a) Maximum in the grade distribution = 100

b) Quarter 3 (Area between median and Q3) has the smallest spread of data.

Spread = 75 - 65 = 10

c) Range of grade distribution = Maximum - Minimum = 100 - 20 = 80

d) More students will be there in 65 - 85 because 45 - 65 and 65 - 75 both covers 25% of the data and in 65 - 85, the students will fall under 75 - 85 will be added over and above 25%.

e) No, the average can't be determined because we don't have individual data values. Also, if the distribution would have been symmetric then we can assume average equals to median but since this is not the case here in the given boxplot, the average can't be determined.

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