Question

2 visual variability and statistics
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: Recall properties of mean and median

The mean is the sum of all data - points divided by the number of data - points. It is affected by extreme values (outliers). The median is the middle - value when the data is arranged in ascending or descending order.

Step2: Analyze box - plot data

Box - plots may have outliers. In the case of these box - plots of miles driven per day, there could be some very high or very low daily mileages (outliers). The mean will be pulled in the direction of these outliers, while the median remains in the middle of the ordered data set and is not affected by outliers. So, the median gives a better representation of the "typical" value of miles driven per day.

Step3: Analyze variability in box - plots

The inter - quartile range (IQR) (the length of the box) and the range (from minimum to maximum) can be used to measure variability. A smaller IQR and range indicate less variability. By observing the box - plots, we can rank them.
Let's assume we observe the lengths of the boxes and the whiskers. If we assume box - plot E has the smallest IQR and range, followed by A, then C, then D, and finally B has the largest IQR and range.

Answer:

a. The median is more appropriate because box - plots may contain outliers, and the mean is sensitive to outliers while the median is not.
b. E, A, C, D, B