justin packed two suitcases for his trip and compared the weights of the items he packed in each of the…
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.
Answer
Explanation:
Step1: Recall box - plot concepts
Box - plot shows minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$) and maximum. Inter - quartile range (IQR)=$Q_3 - Q_1$, range = maximum - minimum.
Step2: Analyze the box - plots visually
For suitcase 1: Minimum is around 4, $Q_1$ is around 8, median is around 10, $Q_3$ is around 12, maximum is around 36. IQR = 12 - 8=4, range = 36 - 4 = 32. For suitcase 2: Minimum is around 4, $Q_1$ is around 6, median is around 10, $Q_3$ is around 14, maximum is around 20. IQR = 14 - 6 = 8, range = 20 - 4=16.
Step3: Evaluate each option
- Option 1: There is no clear outlier in either box - plot.
- Option 2: The median of suitcase 1 and suitcase 2 are both around 10.
- Option 3: IQR of suitcase 1 is 4 and IQR of suitcase 2 is 8, so suitcase 2 has a greater IQR.
- Option 4: Range of suitcase 1 is 32 and range of suitcase 2 is 16. So the data for suitcase 1 has a greater range.