Question

the stem - and - leaf plot below gives sample air fares from st. louis to two cities: denver and cincinnati. there were 14 air fares recorded for the denver route and 17 for the cincinnati route. use the plot to answer the questions.
(a) which route had the greater median air fare?
denver cincinnati the medians were the same
(b) which route had more air fares from $200 to $209?
denver cincinnati each had the same
(c) what were the ranges of air fares for the two routes?
denver $

Explanation:

Step1: Find the median for Denver

For Denver, \(n = 14\) (even). The median is the average of the \(\frac{n}{2}=7^{th}\) and \((\frac{n}{2}+ 1)=8^{th}\) ordered - values.
The ordered data for Denver: \(203,208,213,215,216,220,228,232,234,242,244,251,251,252\)
\(Median_{Denver}=\frac{228 + 232}{2}=230\)

Step2: Find the median for Cincinnati

For Cincinnati, \(n = 17\) (odd). The median is the \(\frac{n + 1}{2}=9^{th}\) ordered - value.
The ordered data for Cincinnati: \(201,219,220,220,224,225,230,233,237,242,245,245,253,254,255,255,256\)
\(Median_{Cincinnati}=237\)

Step3: Compare the medians

Since \(230<237\), Cincinnati has a greater median.

Step4: Count the number of air - fares from \(200\) to \(209\)

For Denver: In the stem - and - leaf plot, the stem \(20\) has \(2\) leaves (\(3\) and \(8\)), so there are \(2\) air - fares from \(200\) to \(209\) for Denver.
For Cincinnati: The stem \(20\) has \(1\) leaf (\(1\)), so there is \(1\) air - fare from \(200\) to \(209\) for Cincinnati.

Step5: Calculate the range for Denver

The range is \(R=\text{Max}-\text{Min}\). For Denver, \(\text{Max}=252\), \(\text{Min}=203\)
\(R_{Denver}=252 - 203=49\)

Answer:

(a) Cincinnati
(b) Denver
(c) \(49\)