Question

1. the boxplot summarizes information about the numbers of hours worked in december for 220 seniors at tomah high school.

a. what is the range? what is the interquartile range?
b. what percent of the students worked 68 or more hours?
c. how many students worked 31 hours or less?
d. does the boxplot give the median of the distribution? what is the median?

Explanation:

Part a

Step1: Calculate Range

Range is maximum minus minimum. From boxplot, max = 80, min = 0.
$Range = 80 - 0$

Step2: Calculate Interquartile Range (IQR)

IQR is $Q_3 - Q_1$. From boxplot, $Q_3 = 68$, $Q_1 = 10$.
$IQR = 68 - 10$

In a boxplot, $Q_3$ (68 here) is the 75th percentile. So data ≥ $Q_3$ is 25% (since 100% - 75% = 25%).

Median (31 here) is the 50th percentile. So 50% of 220 students worked ≤ 31 hours.
$Number\ of\ students = 0.5 \times 220$

Answer:

Range: $80 - 0 = 80$
Interquartile Range: $68 - 10 = 58$

Part b