Question

question: 17
ages of employees at two local restaurants are listed.
restaurant a - 42, 16, 18, 30, 44, 18, 21, 21, 43, 23, 26, 27, 32, 25, 34
restaurant b - 18, 31, 22, 38, 23, 23, 25, 42, 30, 25, 26, 27, 40, 27, 31
part a: determine the interquartile range for restaurant a and restaurant b, and state the difference between the two restaurants. be sure to show and/or explain your work on how you found the interquartile ranges.
part b: identify which restaurant has the larger range and explain how you know.

Explanation:

Step1: Sort data for Restaurant A

16, 18, 18, 21, 21, 23, 25, 26, 27, 30, 32, 34, 42, 43, 44

Step2: Find median (Q2) for Restaurant A

There are 15 data - points. The median is the 8th value. So, Q2(A)=26.

Step3: Find Q1 and Q3 for Restaurant A

The lower half is 16, 18, 18, 21, 21, 23, 25. The median of the lower half (Q1(A)) is 21.
The upper half is 27, 30, 32, 34, 42, 43, 44. The median of the upper half (Q3(A)) is 34.
The inter - quartile range for Restaurant A, IQR(A)=Q3(A) - Q1(A)=34 - 21 = 13.

Step4: Sort data for Restaurant B

18, 22, 23, 23, 25, 25, 26, 27, 27, 30, 31, 31, 38, 40, 42

Step5: Find median (Q2) for Restaurant B

There are 15 data - points. The median is the 8th value. So, Q2(B)=27.

Step6: Find Q1 and Q3 for Restaurant B

The lower half is 18, 22, 23, 23, 25, 25, 26. The median of the lower half (Q1(B)) is 23.
The upper half is 27, 30, 31, 31, 38, 40, 42. The median of the upper half (Q3(B)) is 31.
The inter - quartile range for Restaurant B, IQR(B)=Q3(B) - Q1(B)=31 - 23 = 8.

Step7: Find the difference in IQRs

IQR(A)-IQR(B)

=

13 - 8

= 5.

Step8: Find the range for each restaurant

For Restaurant A, range(A)=44 - 16 = 28.
For Restaurant B, range(B)=42 - 18 = 24.

Answer:

Part A: The inter - quartile range for Restaurant A is 13, for Restaurant B is 8, and the difference between them is 5.
Part B: Restaurant A has the larger range. We know this because the range of Restaurant A is 28 (44 - 16) and the range of Restaurant B is 24 (42 - 18).