To analyze the data set we need to look at:

• Shape: skewed or symmetric
• Center: mean or median
• Spread: range or IQR
• Extreme data points

Because of the extreme data point at 24, this distribution is skewed right.

The mean of the distribution is \frac{12+12+13+13+13+13+13+14+14+24}{10}=14 and the median is 13. The median is a better measure to describe the center of the distribution because the data set is skewed.

The range of the data set is 24-12=12 and the interquartile range is 14-13=1. The interquartile range is a better measure to describe the spread because the data set has an extreme data point that greatly impacts the range.

In summary, the typical age for this data set is 13 years old and the middle half of the ages vary by 1 year. There is an extreme data point at 24 years old making the data set skewed to the right.

Notice that the majority of the data points in the dot plot are between 12-14 years old, but the mean 14.1 and bigger than almost all of the points. This is an example of why the mean shouldn't be used for a skewed data set.

Similarly, if we describe the data set by saying the range is 12 years, it gives the false impression that the data set is spread out over a 12 year span, when in reality most of the data points are 1-2 years apart. This is why it's better to choose the interquartile range to describe the spread of a skewed data set.

To compare these data sets we need to individually identify the:

• Shapes: symmetric or skewed
• Centers: mean and median
• Spread: range and IQR

Both distributions have extreme values that are higher than the rest. Excluding the effect of these outliers, the Chicago Bull's distribution appears to be skew right and the Chicago Sky distribution appears to be symmetric.

The Chicago Bulls have a median weight of 210lbs and the Chicago Sky have a median weight around 165lbs.

The Chicago Bulls have an interquartile range of about 220-190=30\text{lbs}. The range with the extreme data points is about 260-185=75\text{lbs}, but if the extreme values are excluded it's closer to 250-185=65\text{lbs}. The Chicago Sky have an interquartile range of about 185-145=40\text{lbs}. The range with the extreme data point is about 235-135=100\text{lbs}, but the range without the outlier is only about 190-135=55\text{lbs}.

Both teams appear have extreme data values which makes the median and interquartile range a more accurate summary statistic. Excluding the effect of the extreme values, the weight of players on the Chicago Bulls is skewed right which tells us that most players have similar weights and a few players weigh much more than the rest of the team. The weight of players on the Chicago Sky team are symmetrically distributed which tells us that most players weigh around average with a few players weighing less and a few players weighing more.

A typical player on the Chicago Bulls weighs 45lbs more than a typical player on the Chicago Sky which is consistent with the knowledge that men, on average, weigh more than women. The weight of the players on the Chicago Sky basketball team are less consistent than the weights of the players on the Chicago Bulls basketball team because both the range and interquartile range are larger.

When describing and comparing data sets be sure to include a sentence on the shape, center, and spread. Include an analysis of any extreme data points and always include the context of the problem.