The above plot represents the monthly car sales for a year for two sales representatives. We will find the shape of each distribution.
Sales Rep A
For Sales Rep A the whisker lengths are equal and the median is in the middle of the plot. Therefore, the distribution for Sales Rep A is symmetric.
Sales Rep B
For Sales Rep B, the right whisker is longer than the left whisker and most of the data is on the left side of the plot. Therefore, the distribution for Sales Rep B is skewed right.
b To find which representative's sales are more spread out, let's first find the range and interquartile range for each representative. Note that that for Sales Rep A the greatest value is 20 and the least value is 8. For Sales Rep B, the greatest value is 24 and the least value is 4. Let's calculate the difference of each pair of values to find the range.
Sales Rep A's Range: 20- 8=12
Sales Rep B's Range: 24- 4=20
The interquartile range (IQR) is another measure of variation for a data set. It is given by the difference of the third quartile, Q_3, and the first quartile, Q_1. For Sales Rep A Q_3 is 16 and Q_1 is 12. For Sales Rep B, Q_3 is 16 and Q_1 is 8. Let's calculate the difference of each pair of values to find the interquartile range.
Sales Rep A's IQR:& 16- 12=4
Sales Rep B's IQR:& 16- 8=8
Both range and interquartile range of Sales Rep B are greater. Therefore, the monthly car sales for Sales Rep B are more spread out.
c Looking at the given figure, we can see that the least value is 4. This belongs to Sales Rep B. Therefore, Sales Rep B had the single worst sales month during the year.
