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 to the number of calories in each snack pack of trail mix.
number of calories in each snack pack
crackers
trail mix
65 70 75 80 85 90 95 100 105 110 115
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:

1. Analyze the first option: The interquartile range (IQR) of trail mix and range of crackers. IQR is the difference between upper and lower quartiles, range is max - min. Visually, cracker's range (max - min) seems larger than trail mix's IQR, so this is false.
2. Analyze the second option: Outlier in trail mix. For outliers, we use \( Q1 - 1.5\times IQR \) and \( Q3 + 1.5\times IQR \). The trail mix's lower whisker starts at 70, which is within the whisker, so 70 is not an outlier (whiskers include non - outlier data), false.
3. Analyze the third option: Upper quartile of trail mix and max of crackers. From the box - plot, upper quartile of trail mix is around 105, max of crackers is around 100, so false.
4. Analyze the fourth option: Variation (range or spread) of trail mix vs crackers. The trail mix box - plot has a longer whisker (from 70 to 115) and a wider box compared to crackers (from around 70 to 100). So the number of calories in trail mix packs has a greater variation, true.

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.