Question

The boxplot summarizes information about the numbers of hours worked in December for 220

seniors at Tomah High School.
0
10
31
68
80
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?

Answer 1

The range of hours worked is 80, the IQR is 37, 25% of the students worked 68 or more hours, 55 students worked 31 hours or less, and if the boxplot is drawn properly, it should indicate the median.

Step-by-step explanation:

Answering the student's question on interpreting a boxplot, we find the following information about the hours worked by seniors at Tomah High School in December:

• A range can be found by subtracting the smallest value in the dataset from the largest. The given values are 0 and 80, so the range is 80 - 0 = 80 hours.
• The interquartile range (IQR) is calculated by subtracting the first quartile from the third quartile. With the given values of 31 and 68, the IQR is 68 - 31 = 37 hours.
• To find what percent of students worked 68 or more hours, we look at the upper quartile indicating that 75% of the data falls below 68 hours. Therefore, 25% of the students worked 68 or more hours.
• 31 hours or less is represented by the first quartile which contains the lowest 25% of the data. So, 25% of 220 students is 0.25 * 220 = 55 students worked 31 hours or less.
• The median, which is the middle value, is not specifically given, but if the boxplot is symmetrical, the median would often be displayed as the line in the center of the box. If the data is properly summarized, then yes, the median is typically shown in the boxplot.