Question

The following table shows the number of hours some high school students in two towns spend riding the bus each week:

Town A 5 3 9 4 20 9 5 7 6
Town B 8 8 3 5 5 6 3 9 9
Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)

Part B: Are the box plots symmetric? Justify your answer.

Answer 1

To create a five-number summary for the data in Town A and Town B, we need to find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

For Town A:

Minimum: 3

First Quartile (Q1): 5

Median (Q2): 6

Third Quartile (Q3): 9

Maximum: 20

For Town B:

Minimum: 3

First Quartile (Q1): 5

Median (Q2): 6

Third Quartile (Q3): 8

Maximum: 9

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). For Town A, the IQR is 9 - 5 = 4. For Town B, the IQR is 8 - 5 = 3.

Moving on to Part B, to determine if the box plots are symmetric, we need to compare the positions of the median (Q2) and the quartiles (Q1 and Q3) in the box plots. If the median is approximately in the middle of the box and the quartiles are symmetrically placed around the median, then the box plot is considered symmetric.

Based on the five-number summaries we calculated earlier, both Town A and Town B have similar positions for the median (Q2) and quartiles (Q1 and Q3). Therefore, we can conclude that the box plots for both towns are symmetric.

Remember, box plots provide a visual representation of the distribution of data and help us analyze the spread and symmetry of the data.