the randomly selected delivery times, in minutes, of two restaurants are as following. which restaurants has more consistent delivery times?
Restaurant A: 25, 27, 30, 32, 35, 28
Restaurant B: 20, 25, 40, 35, 30, 45
To determine which restaurant has more consistent delivery times, we can calculate the standard deviation of the delivery times for each restaurant. A lower standard deviation indicates more consistent delivery times.
Standard deviation for Restaurant A:
Mean delivery time = (25 + 27 + 30 + 32 + 35 + 28) / 6 = 29.5
Squared deviations from the mean:
(25-29.5)^2 = 21.16
(27-29.5)^2 = 6.25
(30-29.5)^2 = 0.25
(32-29.5)^2 = 6.25
(35-29.5)^2 = 30.25
(28-29.5)^2 = 2.25
Sum of squared deviations = 66.61
Variance = 66.61 / 6 = 11.10167
Standard deviation = √11.10167 = 3.33
Standard deviation for Restaurant B:
Mean delivery time = (20 + 25 + 40 + 35 + 30 + 45) / 6 = 32.5
Squared deviations from the mean:
(20-32.5)^2 = 156.25
(25-32.5)^2 = 56.25
(40-32.5)^2 = 56.25
(35-32.5)^2 = 6.25
(30-32.5)^2 = 6.25
(45-32.5)^2 = 156.25
Sum of squared deviations = 437.5
Variance = 437.5 / 6 = 72.9167
Standard deviation = √72.9167 = 8.54
Based on the standard deviations calculated, Restaurant A has more consistent delivery times compared to Restaurant B.