Question

justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. weights of the items in the two suitcases (in ounces) suitcase 1 suitcase 2 which statement is true about the box plots? the data for suitcase 1 have an outlier, but the data for suitcase 2 does not. the data for suitcase 2 have a greater median than the data for suitcase 1. the data for suitcase 1 has a greater interquartile range than the data for suitcase 2. the data for suitcase 2 has a greater range than the data for suitcase 1.

Explanation:

Step1: Recall box - plot concepts

A box - plot shows the five - number summary (minimum, first quartile $Q_1$, median, third quartile $Q_3$, maximum). The range is $max - min$ and the inter - quartile range (IQR) is $Q_3 - Q_1$.

Step2: Analyze range for each suitcase

For suitcase 1: The minimum value is around 4 and the maximum value is around 20. So the range is approximately $20 - 4=16$.
For suitcase 2: The minimum value is around 4 and the maximum value is around 36. So the range is approximately $36 - 4 = 32$.

Step3: Analyze median

The median is the middle value of the data set. From the box - plot, the median of suitcase 1 is around 10 and the median of suitcase 2 is around 12.

Step4: Analyze inter - quartile range (IQR)

For suitcase 1: $Q_1$ is around 8 and $Q_3$ is around 12, so $IQR_1=12 - 8 = 4$. For suitcase 2: $Q_1$ is around 8 and $Q_3$ is around 20, so $IQR_2=20 - 8=12$.

Step5: Check for outliers

There is no indication of outliers in either box - plot (no points outside the whiskers).

Answer:

The data for suitcase 2 has a greater range than the data for suitcase 1.