Question

1 each box plot summarizes the number of miles driven each day for 30 days in each month. the box plots represent, in order, the months of august, september, october, november, and december.
a
0 10 20 30 40 50 60 70 80 90
miles driven each day in august
b
0 10 20 30 40 50 60 70 80 90
miles driven each day in september
c
0 10 20 30 40 50 60 70 80 90
miles driven each day in october
d
0 10 20 30 40 50 60 70 80 90
miles driven each day in november
e
0 10 20 30 40 50 60 70 80 90
miles driven each day in december
a. the five box plots have the same median. explain why the median is more appropriate for describing the center of the data set than the mean for these distributions.
b. list the box plots in order of least variability to greatest variability. check with another group to see if they agree.

Explanation:

Step1: Understand median and mean

The median is the middle - value when data is ordered. The mean is the sum of all values divided by the number of values. Box - plots show the median as a line within the box.

Step2: Reason for median being better

Box - plots may have outliers. The mean is affected by outliers, while the median is not. So, for skewed distributions or data with outliers (which box - plots may represent), the median is a better measure of central tendency.

Step3: Analyze variability

Variability in box - plots can be measured by the inter - quartile range (IQR, the length of the box) and the range (max - min). A smaller IQR and range indicate less variability.

Step4: Order box - plots

We need to visually inspect the length of the boxes and the whiskers of each box - plot to order them from least to greatest variability.

Answer:

a. The median is more appropriate because box - plots may represent data with outliers or skewed distributions. The mean is sensitive to outliers, while the median is a robust measure of central tendency.
b. Without specific numerical values for IQR and range, we would visually inspect the box - plots. Generally, the box - plot with the shortest box and whiskers has the least variability, and the one with the longest box and whiskers has the greatest variability. We would need to measure the length of the boxes (IQR) and the overall length from minimum to maximum (range) for a more accurate ordering.