Question

Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. A number line goes from 0 to 36. Suitcase 1's whiskers range from 4 to 30, and the box ranges from 8 to 12. A line divides the box at 9. Suitcase 2's whiskers range from 2 to 20, and the box ranges from 5 to 18. A line divides the box at 7. 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 1

Answer:

The correct option is;

The data for suitcase 1 have an outlier but the data for suitcase 2 does not

Step-by-step explanation:

Range of a box plot

Interquartile range (IQR) for bot suitcases we have

Here we have for suitcase 1

IQR = Q₃ - Q₁ = 12 - 8 = 4

For suitcase 2

IQR = Q₃ - Q₁ = 18 - 5 = 13

Lower outlier = Q₁ - 1.5×IQR

Higher outlier = Q₃ + 1.5×IQR

For suitcase 1 we have;

Lower outlier = 8 - 1.5×4 = 2 (No lower outlier)

Higher outlier = 12 + 1.5×4 = 18

Hence, whereby the whiskers range from 4 to 30, suitcase 1 has a higher outlier

For suitcase 2 we have;

Lower outlier = 5 - 1.5×13 = -14.5  (No lower outlier)

Higher outlier = 18 + 1.5×13 = 37.5

Hence, whereby the whiskers range from 2 to 20, suitcase 2 has no outlier.

Therefore, the correct option is the data for suitcase 1 have an outlier but the data for suitcase 2 does not.