Question

1. the school cafeteria takes note of the number of lunches purchased each week by students in first grade. use the box plot to answer the questions.

1st graders
number of lunches purchased each week
a. what is the median number of lunches purchased?
b. half of the first graders purchased ____ or more lunches a week.
c. the interquartile range of the number of lunches purchased each week is ____.
d. what percentage of students purchased their lunch one or more times in a week?

Explanation:

Step1: Recall box - plot properties

The median in a box - plot is the line inside the box. Here, the line inside the box is at 2.

Step2: Understand quartile concepts

The lower quartile ($Q_1$) is the left - hand side of the box. The upper quartile ($Q_3$) is the right - hand side of the box. The inter - quartile range (IQR) is $Q_3 - Q_1$. Here, $Q_1 = 1$ and $Q_3 = 3$, so $IQR=3 - 1=2$.

Step3: Analyze the minimum value

The minimum value of the data set in the box - plot is 0. To find the percentage of students who purchased lunch one or more times, we consider that the total number of students is represented by the whole data set. The number of students who purchased 0 lunches is some part of the data. The percentage of students who purchased 1 or more lunches is $100-\text{percentage of students who purchased 0 lunches}$. Since the minimum is 0 and we assume the data is continuous in terms of frequency, and looking at the box - plot, the percentage of students who purchased 0 lunches is 25% (from the position of the minimum relative to the quartiles). So the percentage of students who purchased 1 or more lunches is 75%.

Answer:

a. 2
b. 1
c. 2
d. 75%