Question

data analysis and probability
using back-to-back stem-and-leaf displays to compare data sets
below gives sample air fares from st. louis to two cities: salt lake city and cincinnati. there were 24 air fare recorded for the salt lake city route and 23 recorded for the cincinnati route. use the display to answer the questions that follow.
air fares (dollars) from st. louis
salt lake city cincinnati
20 | 5 5 2 | 9
21 | 9 4 0 | 5 8
22 | 9 9 8 7 6 4 4 1 0 | 2 5 9 9 9
23 | 9 7 6 5 | 0 3 5 7 7 9
24 | 8 8 7 2 | 1 2 3 3 6 7
25 | 9 | 1 8
key: 20 | 2 → 202 20 | 9 → 209
(a) what were the ranges of air fares for the two routes?
salt lake city $
cincinnati $
(b) which route had the higher median air fare?
salt lake city cincinnati the medians were the same
(c) which route had more air fares from $250 to $259?
salt lake city cincinnati each had the same

Explanation:

Step1: Find the range for Salt Lake City

The range is calculated as \( \text{Max}-\text{Min} \).
For Salt Lake City, the minimum value is \( 202 \) and the maximum value is \( 259 \).
\( 259 - 202=57 \)

Step2: Find the range for Cincinnati

For Cincinnati, the minimum value is \( 209 \) and the maximum value is \( 258 \).
\( 258 - 209 = 49 \)

Step3: Find the median for Salt Lake City

There are \( n = 24 \) data - points. The median is the average of the \( \frac{n}{2}=12^{\text{th}} \) and \( (\frac{n}{2}+1)=13^{\text{th}} \) ordered values.
Counting the values for Salt Lake City:
The \( 12^{\text{th}} \) value is \( 224 \) and the \( 13^{\text{th}} \) value is \( 226 \).
Median \(=\frac{224 + 226}{2}=225 \)

Step4: Find the median for Cincinnati

There are \( n = 23 \) data - points. The median is the \( \frac{n + 1}{2}=12^{\text{th}} \) ordered value.
Counting the values for Cincinnati, the \( 12^{\text{th}} \) value is \( 229 \)

Step5: Count the number of values in the range \( 250 - 259 \)

For Salt Lake City, there is \( 1 \) value (\( 259 \)) in the range \( 250 - 259 \)
For Cincinnati, there are \( 2 \) values (\( 251,258 \)) in the range \( 250 - 259 \)

Answer:

(a) Salt Lake City: \( 57 \), Cincinnati: \( 49 \)
(b) Cincinnati
(c) Cincinnati