The he randomly selected delivery times in mites of two restaurants are as follows . Which restaurant has more consistent delivery times
Restaurant 1 40,37,40,41,38,46,41,37,40
Restaurant 2 42,38,37,39,38,40,42,41,40
To determine which restaurant has more consistent delivery times, we can calculate the standard deviation for each set of delivery times. A lower standard deviation indicates that the delivery times are more consistent.
For Restaurant 1:
Mean = (40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40) / 9 = 39.33
Standard Deviation = √[(40-39.33)² + (37-39.33)² + (40-39.33)² + (41-39.33)² + (38-39.33)² + (46-39.33)² + (41-39.33)² + (37-39.33)² + (40-39.33)²] / 9
= √[(0.33)² + (-2.33)² + (0.33)² + (1.67)² + (-1.33)² + (6.67)² + (1.67)² + (-2.33)² + (0.67)²] / 9
= √[0.1089 + 5.4289 + 0.1089 + 2.7889 + 1.7689 + 44.4889 + 2.7889 + 5.4289 + 0.4489] / 9
= √(63.2491) / 9
= 2.44
For Restaurant 2:
Mean = (42 + 38 + 37 + 39 + 38 + 40 + 42 + 41 + 40) / 9 = 39.33
Standard Deviation = √[(42-39.33)² + (38-39.33)² + (37-39.33)² + (39-39.33)² + (38-39.33)² + (40-39.33)² + (42-39.33)² + (41-39.33)² + (40-39.33)²] / 9
= √[(2.67)² + (-1.33)² + (-2.33)² + (0.67)² + (-1.33)² + (0.67)² + (2.67)² + (1.67)² + (0.67)²] / 9
= √[7.1289 + 1.7689 + 5.4289 + 0.4489 + 1.7689 + 0.4489 + 7.1289 + 2.7889 + 0.4489] / 9
= √(27.2491) / 9
= 1.75
Therefore, Restaurant 2 has more consistent delivery times compared to Restaurant 1 as its standard deviation is lower.