Question

1. ms. moore gathered data from the past 60 days on how many students bought lunch in the cafeteria. the results are show in the box plot below.

a. what percentage of days were there between 240 and 265 students buying lunch?
b. how many days were there between 225 and 265 students buying lunch?
c. what is the range of the data?
d. what is the interquartile range (iqr) of the data?
e. what is the median of the data?

Explanation:

Step1: Recall box - plot properties

A box - plot divides data into quartiles. The box represents the inter - quartile range (IQR), from the first quartile ($Q_1$) to the third quartile ($Q_3$), and the line inside the box is the median.

Step2: Identify quartile values from the box - plot

From the box - plot, we can assume that $Q_1 = 230$, median ($Q_2$) = 240, $Q_3=260$, minimum value = 220, maximum value = 280.

Step3: Answer part a

The IQR (from $Q_1$ to $Q_3$) represents 50% of the data. The range from 240 (median) to 260 ($Q_3$) is half of the IQR. So the percentage of data between 240 and 260 is 25%. Since we want from 240 to 265, and assuming a relatively even distribution in this range, we still consider the percentage from 240 to 260. So the percentage of days with between 240 and 265 students buying lunch is 25%.

Step4: Answer part b

The range from 225 to 265 includes the lower part of the data (from just above the minimum to $Q_3$). The range from 220 to 260 covers 75% of the data. Since we started from 225 instead of 220, we still approximate that the number of days is 75% of 60. $0.75\times60 = 45$ days.

Step5: Answer part c

The range of a data - set is calculated as $Range=Max - Min$. Here, $Max = 280$ and $Min = 220$. So $Range=280 - 220=60$.

Step6: Answer part d

The inter - quartile range (IQR) is calculated as $IQR = Q_3−Q_1$. Here, $Q_1 = 230$ and $Q_3 = 260$. So $IQR=260 - 230 = 30$.

Step7: Answer part e

The median is the value represented by the line inside the box. From the box - plot, the median is 240.

Answer:

a. 25%
b. 45
c. 60
d. 30
e. 240