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 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: Analyze the first option

• For crackers:
• Range = maximum - minimum. From the box - plot, assume minimum \(x_{min,crackers}\approx70\), maximum \(x_{max,crackers}\approx110\). So range \(R_{crackers}=110 - 70=40\).
• For trail - mix:
• Inter - quartile range \(IQR = Q_{3}-Q_{1}\). Assume \(Q_{1,tm}\approx90\), \(Q_{3,tm}\approx105\). So \(IQR_{tm}=105 - 90 = 15\). Since \(15<40\), the first option is false.

Step2: Analyze the second option

• To check for an outlier in trail - mix data:
• The formula for an outlier is \(x Q_{3}+1.5\times IQR\).
• \(Q_{1,tm}\approx90\), \(IQR_{tm}=15\), \(Q_{1}-1.5\times IQR=90-1.5\times15=90 - 22.5 = 67.5\), \(Q_{3}+1.5\times IQR=105 + 22.5=127.5\). Since \(70>67.5\), 70 is not an outlier. So the second option is false.

Step3: Analyze the third option

• For trail - mix, \(Q_{3,tm}\approx105\). For crackers, \(x_{max,crackers}\approx110\). Since \(105

eq110\), the third option is false.

Step4: Analyze the fourth option

• For crackers:
• Range \(R_{crackers}=110 - 70 = 40\).
• For trail - mix:
• Range \(R_{tm}=115 - 70=45\). Since \(45>40\), the number of calories in the packs of trail mix have a greater variation (as range is a measure of variation) than the number of calories in the packs of crackers.

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.