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 sort the delivery times in ascending order.

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

Since there are 8 delivery times (an even number), the median is calculated by taking the average of the 4th and 5th values:

• 4th value: 21
• 5th value: 22

Median for Pizza Shop 1: \[ \text{Median} = \frac{21 + 22}{2} = \frac{43}{2} = 21.5 \text{ minutes} \]

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

Again, with 8 delivery times (even), the median is the average of the 4th and 5th values:

• 4th value: 20
• 5th value: 20

Median for Pizza Shop 2: \[ \text{Median} = \frac{20 + 20}{2} = \frac{40}{2} = 20 \text{ minutes} \]

Conclusion:

• 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.

Final answers: 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.