Kat and Joshua want to know which pizza shop has the fastest delivery time. Kat took a random sample of 8 delivery times from pizza shop 1 over a period of six months. Joshua did the same for pizza shop 2. The delivery times (in minutes) for each pizza shop are shown in the following table.

Question

This table displays the delivery times (in minutes) for two different pizza shops.
Pizza Shop 1 Pizza Shop 2
18 20
23 17
15 16
22 38
21 21
24 20
28 18
20 25
Find the median delivery time for each pizza shop. Based on the median, which pizza shop has the fastest delivery time? Express your answer as a decimal if needed. Do not round your answer.

(2 points)
The median delivery time of Pizza Shop 1 is
minutes. The median delivery time of Pizza Shop 2 is
minutes. Based on the median, Pizza Shop
has a faster delivery time.

Answer 1

To find the median delivery time for each pizza shop, we first need to arrange the delivery times in ascending order.

Pizza Shop 1 delivery times: 18, 23, 15, 22, 21, 24, 28, 20

• Arranged: 15, 18, 20, 21, 22, 23, 24, 28

There are 8 data points (even number), so the median is the average of the middle two numbers (the 4th and 5th values).

• Middle values: 21 and 22
• Median for Pizza Shop 1 = (21 + 22) / 2 = 21.5 minutes

Pizza Shop 2 delivery times: 20, 17, 16, 38, 21, 20, 18, 25

• Arranged: 16, 17, 18, 20, 20, 21, 25, 38

Similarly, with 8 data points, we take the average of the 4th and 5th values.

• Middle values: 20 and 20
• Median for Pizza Shop 2 = (20 + 20) / 2 = 20 minutes

Now we can summarize:

• The median delivery time of Pizza Shop 1 is 21.5 minutes.
• The median delivery time of Pizza Shop 2 is 20 minutes.

Based on the median, Pizza Shop 2 has a faster delivery time.