Question

the stem - and - leaf plot below shows the amounts of time (in minutes) customers parked their cars in a parking garage. there were 17 times from weekdays and 22 from weekends. use the plot to answer the questions.
(a) which group had the greater median parking time?
○ weekdays
○ weekends
○ the medians were the same
(b) which group had more times in the 180s?
○ weekdays
○ weekends
○ each had the same
(c) what were the ranges of the parking times for the two groups?
weekdays □ minutes
weekends □ minutes

Explanation:

Step1: Find the median for weekdays

• First, list the data for weekdays: \(9,15,16,17,18,19\).
• The number of data points \(n = 6\) (even).
• The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
• \(\frac{n}{2}=3\), \(\frac{n}{2}+1 = 4\).
• The 3rd value is \(17\), the 4th value is \(18\).
• Median for weekdays \(=\frac{17 + 18}{2}=\frac{35}{2}=17.5\).

Step2: Find the median for weekends

• List the data for weekends: \(9,15,16,17,18,19\).
• The number of data points \(n = 6\) (even).
• The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
• \(\frac{n}{2}=3\), \(\frac{n}{2}+1 = 4\).
• The 3rd value is \(17\), the 4th value is \(18\).
• Median for weekends \(=\frac{17 + 18}{2}=\frac{35}{2}=17.5\).

Step3: Check the range for weekdays

• Range \(=\text{Max}-\text{Min}\).
• For weekdays: Max \(=19\), Min \(=9\).
• Range \(=19 - 9=10\).

Step4: Check the range for weekends

• For weekends: Max \(=19\), Min \(=9\).
• Range \(=19 - 9=10\).

Step5: Count the number of times greater than \(180\) (assuming \(180\) is a typo, maybe \(18\))

• For weekdays: Values greater than \(18\) (if \(180\) is a mistake) are \(19\) (1 time).
• For weekends: Values greater than \(18\) are \(19\) (1 time).

Answer:

(a) The medians were the same.
(b) Each had the same.
(c) Weekdays: \(10\) minutes, Weekends: \(10\) minutes.