wait time (in minutes) first restaurant second restaurant 8 7|0|5 9 8 7 5 2 2 1 1|1|2 4 7 9 8 7 2|2|0 2 4 4…

Explanation:

Step1: List data for first restaurant

The data set for the first - restaurant is (7,8,11,11,12,12,15,17,18,22,27,28,29,33,37,39,43,44,45). There are (n = 19) data points. The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{19+1}{2}=10) - th value. So the median of the first - restaurant is (22).

Step2: List data for second restaurant

The data set for the second - restaurant is (5,9,12,14,17,20,22,24,24,27,30,31,35,37,40,41,45,45). There are (n = 18) data points. The median is the average of the (\frac{n}{2})-th and (\left(\frac{n}{2}+1\right))-th values. (\frac{18}{2}=9) and (\frac{18}{2}+1 = 10). The 9 - th value is (24) and the 10 - th value is (27). So the median is (\frac{24 + 27}{2}=25.5). Since (25.5>22), the second restaurant has the greater median.

Step3: Calculate range for first restaurant

The range is the difference between the maximum and minimum values. For the first restaurant, the minimum value is (7) and the maximum value is (45). So the range is (45−7 = 38).

Step4: Calculate range for second restaurant

For the second restaurant, the minimum value is (5) and the maximum value is (45). So the range is (45−5 = 40).

Step5: Count wait - times from 10 to 19 for first restaurant

For the first restaurant, the wait - times in the 10 - 19 range are (11,11,12,12,15,17,18), so there are (7) values.

Step6: Count wait - times from 10 to 19 for second restaurant

For the second restaurant, the wait - times in the 10 - 19 range are (12,14,17), so there are (3) values. The first restaurant has more wait - times in the 10 - 19 range.

Answer:

(a) Second restaurant (b) First restaurant: (38) minutes, Second restaurant: (40) minutes (c) First restaurant