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.
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?
(2 points)
For Pizza Shop 1:
Delivery times: 18, 23, 15, 22, 21, 24, 28, 20
Arrange in ascending order: 15, 18, 20, 21, 22, 23, 24, 28
Median = (20 + 21) / 2 = 20.5
For Pizza Shop 2:
Delivery times: 20, 17, 16, 38, 21, 20, 18, 25
Arrange in ascending order: 16, 17, 18, 20, 20, 21, 25, 38
Median = (20 + 21) / 2 = 20.5
Based on the medians, both Pizza Shop 1 and Pizza Shop 2 have the same median delivery time of 20.5 minutes, so they have the same speed of delivery.
Pizza shop 1 is wrong
Apologies for the error in the previous calculation for Pizza Shop 1. Let's recalculate the median for Pizza Shop 1:
For Pizza Shop 1:
Delivery times: 18, 23, 15, 22, 21, 24, 28, 20
Arrange in ascending order: 15, 18, 20, 21, 22, 23, 24, 28
Since the sample size is 8 (even number):
The median will be the average of the two middle numbers:
Median = (21 + 22) / 2 = 21.5
For Pizza Shop 2:
Delivery times: 20, 17, 16, 38, 21, 20, 18, 25
Arrange in ascending order: 16, 17, 18, 20, 20, 21, 25, 38
Median = (20 + 21) / 2 = 20.5
So, based on the corrected medians, Pizza Shop 2 has the fastest delivery time with a median delivery time of 20.5 minutes, compared to Pizza Shop 1 with a median delivery time of 21.5 minutes.
Pizza shop 1 time has to be lower than pizza shop 2
Apologies for the oversight. Let's recalculate the medians for both Pizza Shop 1 and Pizza Shop 2:
For Pizza Shop 1:
Delivery times: 18, 23, 15, 22, 21, 24, 28, 20
Arrange in ascending order: 15, 18, 20, 21, 22, 23, 24, 28
Since the sample size is 8 (even number):
The median will be the average of the two middle numbers:
Median = (21 + 22) / 2 = 21.5
For Pizza Shop 2:
Delivery times: 20, 17, 16, 38, 21, 20, 18, 25
Arrange in ascending order: 16, 17, 18, 20, 20, 21, 25, 38
Median = (20 + 21) / 2 = 20.5
Based on the corrected medians, Pizza Shop 2 still has the fastest delivery time with a median delivery time of 20.5 minutes, compared to Pizza Shop 1 with a median delivery time of 21.5 minutes. Thank you for pointing out the error.