Question

1. the test grades of 40 different students were used to create the box-and-whisker below. answer the following questions.

test grades
a. what is the lowest test score? highest?
b. what is the interquartile range?
c. approximately, how many students scored an 81.5 or higher on the test?
d. approximately, how many students scored lower than 77?

Explanation:

Step1: Identify min/max from plot

Lowest score: left whisker end = 72; Highest score: right whisker end = 99

Step2: Calculate interquartile range

Interquartile range = Q3 - Q1 = $90 - 76 = 14$

Step3: Find students with score ≥81.5

81.5 is Q2 (median). 50% of 40 students: $\frac{50}{100} \times 40 = 20$

Step4: Find students with score <77

77 is between Q1 (76) and min (72). This is 25% of data: $\frac{25}{100} \times 40 = 10$

Answer:

a. Lowest test score: 72; Highest test score: 99
b. 14
c. 20
d. 10