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)
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 2
has a faster delivery time.
To find the median delivery time for each pizza shop, we first need to arrange the delivery times in each shop in ascending order:
For Pizza Shop 1: 15, 18, 20, 21, 22, 23, 24, 28
For Pizza Shop 2: 16, 17, 18, 20, 20, 21, 25, 38
Since there is an even number of delivery times for Pizza Shop 1, the median is the average of the two middle values, which are 21 and 22. So, the median delivery time for Pizza Shop 1 is (21+22)/2 = 21.5 minutes.
For Pizza Shop 2, since there is an odd number of delivery times, the median is the middle value, which is 20 minutes.
Based on the median delivery times, Pizza Shop 2 has the faster delivery time as its median delivery time is lower than that of Pizza Shop 1.