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
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.
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 of a data set when ordered. The mean is the sum of all values divided by the number of values.

Step2: Consider skewness and outliers

Box - plots can show skewness and outliers. If a distribution has outliers or is skewed, the mean can be pulled in the direction of the outliers or the long - tail of the skewness. The median is not affected by extreme values. In the context of daily miles driven, there could be days with very high or very low miles (outliers). For example, a long road trip on one day (high outlier) or a day when the car wasn't used (low outlier) would affect the mean but not the median. So, the median is a better measure of the center as it represents the middle value of the ordered data set and is more robust to outliers.

Step3: Analyze variability

Variability in a box - plot can be judged by the length of the box (IQR: Inter - Quartile Range) and the length of the whiskers. A shorter box and shorter whiskers indicate less variability.

Answer:

The median is more appropriate than the mean for these distributions because the data may contain outliers (such as days with very high or very low miles driven) which would affect the mean but not the median. To order the box - plots from least variability to greatest variability, we need to look at the lengths of the boxes (IQR) and the whiskers. The box - plot with the shortest box and shortest whiskers has the least variability and the one with the longest box and longest whiskers has the greatest variability. Without specific numerical values for the IQR and whisker lengths, we can visually estimate. But in general, we compare the spread of the middle 50% (IQR) and the overall range (including whiskers) of each box - plot.