One way to compare distributions to one another is to locate the center of each. The distributions for Long Life and Super Charge have middle values where the data tend to cluster. Means computed from random samples of a population tend to cluster like this.
After looking at a dot plot to see if there is a central cluster, it can be helpful to compute a measure of center such as the median, and to create a box plot. The box plot below shows that the median for the Long Life distribution is 15. You can make a box plot to show the median for the Super Charge distribution is 20.
Long
Life
Since the median values fall within the central clusters, they do a good job of representing the typical values for each distribution. The difference in centers suggests that Super Charge is the longer-lasting brand.
Sometimes we also want to know how spread out a data set is (its variability). The smaller the spread, the more alike the battery lives are. One formal measure of variability is the interquartile range (IQR). In a box plot, it’s the distance from the first to the third quartile. The interquartile range for each battery brand in our example is 2. This tells us that the middle 50% of the data lie within 2 units of one another. So, we can expect the same amount of consistency from each brand.
Reflect
1 Compute the means for the Super Charge and Long Life distributions. Is the mean a good number for describing the center of each distribution? Why or why not?
so, did you calculate the means?
How do they compare with the medians?