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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. 

"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.

1 answer

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

Pizza Shop 1 Delivery Times:

  • Original: 18, 23, 15, 22, 21, 24, 28, 20
  • Sorted: 15, 18, 20, 21, 22, 23, 24, 28

Finding the Median for Pizza Shop 1: Since there are 8 data points (an even number), the median will be the average of the 4th and 5th values in the sorted list.

  • 4th value: 21
  • 5th value: 22

Median for Pizza Shop 1 = (21 + 22) / 2 = 21.5 minutes.

Pizza Shop 2 Delivery Times:

  • Original: 20, 17, 16, 38, 21, 20, 18, 25
  • Sorted: 16, 17, 18, 20, 20, 21, 25, 38

Finding the Median for Pizza Shop 2: Again, since there are 8 data points (even), the median is the average of the 4th and 5th values in the sorted list.

  • 4th value: 20
  • 5th value: 20

Median for Pizza Shop 2 = (20 + 20) / 2 = 20 minutes.

Summary:

  • The median delivery time for Pizza Shop 1 is 21.5 minutes.
  • The median delivery time for Pizza Shop 2 is 20 minutes.
  • Based on the median, Pizza Shop 2 has a faster delivery time.

So filling in the blanks:

  • 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.