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

Question

The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 500 students. 4. 20 45 65 75 100 10 20 3040506070 80 90 100 Answer each question based on the given information, and explatn 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 in the grade distribution = left whisker

minimum in the grade distribution = 20

b) Spread of first quarter = 45-20 = 25

Spread of second quarter = 65-45 = 20

Spread of third quarter = 75-65 = 10

Spread of fourth quarter = 100 - 75 = 25

So the third quarter have the smallest spread which is of 10 units.

c) IQR = Range of box

IQR = 75-45 = 30

d) There are more students in 60-80 range because between 60-80 a whole quarter is included, while in 20-40 not even one quarter is present

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