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 each option:

• Option 1: The interquartile range (IQR) of trail mix and range of crackers. IQR is Q3 - Q1, range is max - min. From box plots, trail mix IQR is less than cracker range (cracker range: ~100 - 70 = 30; trail mix IQR: ~105 - 90 = 15), so false.
• Option 2: For outliers, we use 1.5IQR rule. Trail mix Q1 is 90, Q3 is 105, IQR = 15. Lower fence: 90 - 1.515 = 67.5. 70 > 67.5, not an outlier, so false.
• Option 3: Trail mix upper quartile (Q3) is 105, cracker maximum is 100, not equal, so false.
• Option 4: Variation is seen in range or IQR. Cracker range: ~100 - 70 = 30; Trail mix range: ~115 - 70 = 45. Trail mix has greater variation, so 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.