Question

2.a commuter travels many miles to work each morning. she has timed this trip 5 times during the last month. the time (in minutes) required to make this trip was 38, 33, 36, 47, and 41. what is the variance for this sample data?

Answer 1

The variance for the commuter's sample travel time data is 28.5 minutes squared, calculated using the steps of determining the mean, finding the squared differences from the mean, and then dividing the sum of these squares by 4 (the sample size minus one).

Step-by-step explanation:

The commuter has taken 5 trips with times of 38, 33, 36, 47, and 41 minutes. To find the variance of this sample data, we first calculate the mean (average) of these times. Then we subtract the mean from each of the times, square these differences, sum them, and finally divide by the number of observations minus one (since this is a sample variance).

Calculate the mean: (38 + 33 + 36 + 47 + 41) / 5 = 195 / 5 = 39 minutes.

Subtract each time from the mean, square the result, and sum these values:
`(38 - 39)^2 + (33 - 39)^2 + (36 - 39)^2 + (47 - 39)^2 + (41 - 39)^2` = 1 + 36 + 9 + 64 + 4 = 114.

Divide by the number of observations minus one: 114 / (5 - 1) = 114 / 4 = 28.5.

The sample variance for the commuter's travel time is 28.5 minutes squared.