The five-number summary below shows the grade distribution of a quiz for a sampl

Question

The five-number summary below shows the grade distribution of a quiz for a sample of 500 students.

20 65 75 100 0 10 20 30 40 50 60 70 8o 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) 20 is the minimum

b) Third quarter as it has the smallest width(median to third quartile), spread = 75 - 65 = 10

c) IQR = 75 - 45 = 30

d) There are more students in the 60-80 band as the median is pulled towards that direction and lies more towards 60-80 band

e) No mean cannot be found as we require all 500 scores to do that.

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