a variety of two types of snack packs are delivered to a store. the box plots compare the number of calories…

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.\nnumber of calories in each snack pack\ncrackers\ntrail mix\nwhich statement is true about the box plots?\nthe interquartile range of the trail mix data is greater than the range of the cracker data.\nthe value 70 is an outlier in the trail mix data.\nthe upper quartile of the trail mix data is equal to the maximum value of the cracker data.\nthe number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

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.\nnumber of calories in each snack pack\ncrackers\ntrail mix\nwhich statement is true about the box plots?\nthe interquartile range of the trail mix data is greater than the range of the cracker data.\nthe value 70 is an outlier in the trail mix data.\nthe upper quartile of the trail mix data is equal to the maximum value of the cracker data.\nthe number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer

Explanation:

Step1: Recall box - plot concepts

For a box - plot, the range is (max - min), and the inter - quartile range (IQR) is (Q_3 - Q_1). Variation can be measured by range or IQR. An outlier is a value that lies outside the whiskers of the box - plot.

Step2: Analyze the crackers box - plot

For crackers: (min\approx70), (Q_1\approx75), (Q_2\approx80), (Q_3\approx85), (max\approx90). Range of crackers (=90 - 70=20), (IQR_{crackers}=85 - 75 = 10).

Step3: Analyze the trail mix box - plot

For trail mix: (min\approx70), (Q_1\approx90), (Q_2\approx95), (Q_3\approx105), (max\approx115). Range of trail mix (=115 - 70 = 45), (IQR_{trail\ mix}=105 - 90=15).

Step4: Evaluate each statement

  • Statement 1: (IQR_{trail\ mix}=15), range of crackers ( = 20), so (IQR_{trail\ mix}<\text{range of crackers}), this statement is false.
  • Statement 2: The value 70 is the minimum of the trail - mix data and is not an outlier. Outliers are typically defined as values less than (Q_1-1.5\times IQR) or greater than (Q_3 + 1.5\times IQR). For trail mix, (Q_1 - 1.5\times IQR=90-1.5\times15=90 - 22.5 = 67.5), and 70 is not less than 67.5, so this statement is false.
  • Statement 3: The upper quartile of trail mix ((Q_3 = 105)) and the maximum value of crackers ((max = 90)), (105\neq90), so this statement is false.
  • Statement 4: The range of trail mix is 45 and the range of crackers is 20. Since (45>20), the number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers. This statement is 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.