Question

a variety of two types of snack packs are delivered to a store. the box plots compare the number of calories in each snack pack of crackers and the number of calories in each snack pack of trail mix. which statement is true about the box plots? the interquartile range of the trail mix data is greater than the range of the cracker data. the value 70 is an outlier in the trail mix data. the upper quartile of the trail mix data is equal to the maximum value of the cracker data. the number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Explanation:

Step1: Recall box - plot concepts

A box - plot shows the five - number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. The inter - quartile range (IQR) is $Q_3 - Q_1$. An outlier is a value less than $Q_1-1.5\times IQR$ or greater than $Q_3 + 1.5\times IQR$.

Step2: Analyze the trail - mix box - plot

For the trail - mix data:

• The minimum is around 70, $Q_1$ is around 80, $Q_2$ is around 90, $Q_3$ is around 95, and the maximum is around 115.
• The IQR for trail - mix is $Q_3 - Q_1=95 - 80 = 15$.
• Lower fence for outliers in trail - mix is $Q_1-1.5\times IQR=80-1.5\times15=80 - 22.5 = 57.5$. Upper fence for outliers in trail - mix is $Q_3+1.5\times IQR=95 + 1.5\times15=95+22.5 = 117.5$. Since 70 is within the range of non - outliers (57.5 - 117.5), 70 is not an outlier.
• The inter - quartile range of trail - mix ($IQR_{trail - mix}=15$). For crackers, assume minimum is around 65, $Q_1$ is around 75, $Q_2$ is around 80, $Q_3$ is around 85, and maximum is around 90. The IQR for crackers is $Q_3 - Q_1=85 - 75 = 10$. So the IQR of trail - mix is greater than the IQR of crackers.
• The upper quartile of trail - mix (95) is not equal to the maximum value of the cracker data (90).
• The number of calories in the packs of trail - mix has a greater variation (as measured by the range and IQR) than the number of calories in the packs of crackers. The range of trail - mix is $115 - 70=45$ and the range of crackers is $90 - 65 = 25$.

Answer:

The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.