Begin by finding the distribution and measures that best represent each data set.
See solution.
Practice makes perfect
Consider the given double histogram. The given figure shows the distribution of daily high temperatures for two towns over a 50-day period.
We are asked to compare the data distribution by using their shapes and appropriate measures of center and variation. To do so, let's first find the distribution of each histogram and the measures that best represent each data set. Then we will compare the center and variation of the data sets.
Distribution and Measures
Town A Histogram
We can see that most of the data are on the right of the distribution and the tail of the graph extends to the left, so the distribution is skewed left. Therefore, the median and the five-number summary best represent the center and distribution for Town A.
Town B Histogram
We can see that the data on the right of the distribution are approximately a mirror image of the data on the left of the distribution., so the distribution is symmetric. Therefore, the mean and the standard deviation best represent the center and distribution for Town B.
Comparison
Center
The median of the Town A data set is in the 70-79 interval, while the mean of the Town B data set is probably in the 60-69 interval. This means that a typical day is much more likely to have a higher temperature in Town A than in Town B.
Variation
The data for Town B is more variable than the data for Town A. This means that the daily high temperature tends to differ more for Town B.
