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 0 10 20 3040 50600 607o 50 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 in the grade distribution. (d) Are there more students in the score band of 45- 65 or 65-85? Why? (e) Can the average score be determined based on the given information? Why or why not?

Explanation / Answer

a)

Minimum value in the distribution is 20.

b)

Data between Q2 and Q3 has smallest spread.

Spread is 75-65 = 10

c)

Interquartile range is q3-q1 = 75-45 = 30

d)

65-85 band have more number of students. Because 45 to 65 has 25 percentile of the data. But 65 to 75 itself have 25 percentile of the data.

e)

From the box plot we cannot claculate mean. We can find median and some other details like minimum, max, q1 and q3

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