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

ID: 2927243 • Letter: T

Question

The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 500 students.

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?

20 45 65 75 100 0 10 20 30 40 50 60 70 80 90 100

From the given five number summary:

Minimum value = 20

First quartile = Q1 = 45

Median = Q2 = 65

Third quartile = Q3 = 75

Maximum value = 100

(a) Minimum value = 29

(b)

Quarter Spread

First Quarter 45-20=25

Second Quarter 65 - 45 = 20

Third Quarter 75 - 65 = 10

Fourh Quarter 100 - 75 = 25

Thid quarter has the smallest spread. Spread = 10

(d) There are more students in the score band of 20 - 40, since the spread is more in this band.

(e) Average score cannot be determined because all the scores are required to calculate the average.

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