Question

a stem - and - leaf display below gives the number of minutes that customers waited for their orders at two different restaurants. there were 22 wait times recorded for the first restaurant and 23 recorded for the second. use the display to answer the questions that follow.
number of minutes customers waited
first restaurant second restaurant
8 5 | 0 | 6 7 8 8 9
7 7 2 0 0 | 1 | 3 4 5 6 7 7 7 8
4 4 3 2 0 0 | 2 | 2 4 4 6 6 8
7 4 4 1 1 | 3 | 5 5 7
7 5 3 1 | 4 | 4
key: 5 - 5|0|6 → 6
(a) what were the ranges of wait times for the two restaurants?
first restaurant
second restaurant
(b) which restaurant had the greater median wait time?
first restaurant second restaurant the medians were the same
(c) which restaurant had more wait times from 40 to 49 minutes?

Explanation:

Step1: Find range for first restaurant

Range = Max - Min. Max is 47 (from 4|7 in stem - leaf), Min is 5 (from 0|5). So range is $47 - 5=42$.

Step2: Find range for second restaurant

Max is 44 (from 4|4 in stem - leaf), Min is 6 (from 0|6). So range is $44 - 6 = 38$.

Step3: Find median for first restaurant

There are 22 data - points. Median is average of 11th and 12th ordered values. Ordering the data from stem - leaf, 11th and 12th values are 22 and 23. Median is $\frac{22 + 23}{2}=22.5$.

Step4: Find median for second restaurant

There are 23 data - points. Median is 12th ordered value. Ordering the data from stem - leaf, 12th value is 17.

Step5: Count wait - times from 40 - 49 for first restaurant

There are 4 values (41, 43, 45, 47) in the 4 - stem of first restaurant's stem - leaf.

Step6: Count wait - times from 40 - 49 for second restaurant

There is 1 value (44) in the 4 - stem of second restaurant's stem - leaf.

Answer:

(a) First restaurant: 42, Second restaurant: 38
(b) First restaurant
(c) First restaurant