Question

(a) what were the ranges of wait times for the two restaurants? first restaurant second restaurant (b) which restaurant had more wait times from 10 to 19 minutes? first restaurant second restaurant each had the same (c) which restaurant had the greater median wait time? first restaurant second restaurant the medians were the same

Explanation:

Step1: Find the range for each restaurant

• First restaurant:
• The minimum value is \(7\) (from \(9|7\) in the stem - and - leaf plot, where the stem is \(9\) and the leaf is \(7\), representing \(97\) is incorrect, actually, in a stem - and - leaf plot for single - digit stems: if the stem is \(9\) and leaf is \(7\), it's \(9.7\) which is wrong. Wait, no, for wait - time (assuming two - digit numbers). First restaurant: the data points are \(7,8,9,10,12,12,12,13,16,17\) (from the stem - and - leaf plot: stem \(9\) (wait, no, if we consider the stem as the tens digit. First restaurant: stem \(9\) (tens digit \(9\)) with leaf \(7\) (units digit \(7\)) gives \(97\) which is wrong. Wait, no, for wait - time in minutes, assume the stem is the tens digit. First restaurant: \(7,8,9,10,12,12,12,13,16,17\) (from the stem - and - leaf: \(9|7\) is \(97\) no, wait, no, if the stem is the tens digit. Wait, no, for the first restaurant: the data is \(7,8,9,10,12,12,12,13,16,17\). The range is \(R_1=\text{Max}-\text{Min}=17 - 7=10\)
• Second restaurant:
• The data points are \(10,12,14,16,20,22,24,26,27,32\) (from the stem - and - leaf plot: stem \(10\) (tens digit \(10\)) is wrong. Wait, no, if we consider the stem as the tens digit. Second restaurant: \(10,12,14,16,20,22,24,26,27,32\). The range is \(R_2=\text{Max}-\text{Min}=32 - 10 = 22\)

Step2: Find the median for each restaurant

• First restaurant:
• Since \(n = 10\) (even number of data points). The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The \(5\)th value is \(12\) and the \(6\)th value is \(12\). So, \(M_1=\frac{12 + 12}{2}=12\)
• Second restaurant:
• Since \(n = 10\) (even number of data points). \(\frac{n}{2}=5\) and \(\frac{n}{2}+1=6\). The \(5\)th value is \(20\) and the \(6\)th value is \(22\). So, \(M_2=\frac{20+22}{2}=21\)

Step3: Check the number of data points in the \(10 - 19\) range

• First restaurant:
• The data points in the \(10 - 19\) range are \(10,12,12,12,13,16,17\) (7 data points)
• Second restaurant:
• The data points in the \(10 - 19\) range are \(10,12,14,16\) (4 data points)

Answer:

(a) First restaurant: \(10\) minutes, Second restaurant: \(22\) minutes; (b) First restaurant; (c) Second restaurant