We will begin by looking at the for the entrées in certain price ranges (in dollars) for Restaurant A.
| Restaurant B
|
| Price Range
|
Frequency
|
| 8-10
|
0
|
| 11-13
|
2
|
| 14-16
|
5
|
| 17-19
|
7
|
| 20-22
|
8
|
| 23-25
|
6
|
We are asked to display the in a double . Then we will compare the distributions using their shapes and appropriate and . Let's first make the histograms.
Histograms
To make the double histogram, we will split the vertical axis into two equal parts. This will represent the frequency. In the top half will be the histogram for Restaurant A, while in the bottom half we will put the histogram for Restaurant B. Let's do it!
Distribution and Measures
Restaurant A Histogram
We can see that most of the data are on the left of the distribution and the tail of the graph extends to the right. Then the is . Therefore, the and the five-number summary best represent the center and distribution for Restaurant A.
Restaurant B 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. Then the distribution is . Therefore, the median and the five-number summary best represent the center and distribution for Restaurant B.
Comparison
Center
The median of the Restaurant A data set is in the 14-16 interval, while the mean of the Restaurant B data set is between the 17-19 and 20-22 interval. This means that entrées prices from Restaurant B are typically higher.
Variation
Observing the histograms, we can see that for Restaurant A most of the prices are concentrated in the two middle bars, while for Restaurant B the data is more spread out. This means that the entrée prices tends to differ more for Restaurant B.
