Question

the stem - and - leaf plot below gives the number of minutes that customers waited for their orders at two restaurants. there were 18 wait times recorded for the first restaurant and 19 for the second. use the plot to answer the questions.
(a) which restaurant had the greater median wait time?
first restaurant
second restaurant
the medians were the same
(b) which restaurant had more wait times from 10 to 19 minutes?
first restaurant
second restaurant
each had the same
(c) what were the ranges of wait times for the two restaurants?
first restaurant
minutes
second restaurant
minutes

Explanation:

Step1: Find the median for the first restaurant

For the first restaurant, the data set is \(8,8,10,11,14,15,15,15,18\). Since there are \(n = 9\) data points, the median is the \(\frac{n + 1}{2}\) -th value. \(\frac{9+1}{2}=5\) -th value. The \(5\) -th value is \(14\).

Step2: Find the median for the second restaurant

For the second restaurant, the data set is \(10,12,12,12,15,16,17,19,19,19\). Since there are \(n = 10\) data points, the median is the average of the \(\frac{n}{2}\) -th and \((\frac{n}{2}+1)\) -th values. \(\frac{10}{2}=5\) and \(\frac{10}{2}+1 = 6\). The \(5\) -th value is \(15\) and the \(6\) -th value is \(16\). The median is \(\frac{15 + 16}{2}=15.5\). So the second restaurant has a greater median.

Step3: Check part (b)

For the first restaurant, count the number of values from \(10\) to \(19\). The values are \(10,11,14,15,15,15,18\) (7 values). For the second restaurant, the values from \(10\) to \(19\) are \(10,12,12,12,15,16,17,19,19,19\) (10 values). So the second restaurant has more wait times from \(10\) to \(19\) minutes.

Step4: Check part (c)

For the first restaurant, the minimum is \(8\) and the maximum is \(18\). The range is \(18−8 = 10\). For the second restaurant, the minimum is \(10\) and the maximum is \(19\). The range is \(19−10=9\).

Answer:

(a) Second restaurant \(\square\) minutes, First restaurant \(\square\) minutes; (b) Second restaurant; (c) First restaurant: \(10\) minutes, Second restaurant: \(9\) minutes.