Distribution: The distribution for Shop A and Shop B is skewed right. More Spread Out? Shop A, see solution.
Practice makes perfect
Consider the given double box-and-whisker plot for the surfboard prices at Shop A and Shop B.
We are asked to find each distribution's shape and which shop's prices are more spread out. Let's find one at a time.
Distribution's Shape
We can see that for Shop A, the right whisker is longer than the left whisker and most of the data is on the left side of the plot. Additionally, for Shop B the right whisker is also longer than the left one and most of the data is on the left side of the plot. Therefore, the distribution for Shop A and Shop B is skewed right.
More Spread Out
To find which shop's prices are more spread out, let's first find the range and interquartile range for each shop. Note that for Shop A the greatest value is $900 and the least value is $300. For Shop B, the greatest value is $600 and the least value is $250. Let's calculate the difference of each pair of values to find the range.
Shop A's Range: 900- 300=$600
Shop B's Range: 600- 250=$350
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. It represents the range of the middle half of the data. For Shop A, Q_3 is 600 and Q_1 is 400. For Shop B, Q_3 is 450 and Q_1 is 300. Let's calculate the difference of each pair of values to find the interquartile range.
Shop A's IQR: 600- 400=$200
Shop B's IQR: 450- 300=$150
Both the range and the interquartile range of Shop A are greater. Therefore, Shop A's prices are more spread out.
