Question

The checkout times (in minutes) for 12

randomly selected customers at a large supermarket during the store’s busiest time are:
4.6, 8.5, 6.1, 7.8, 10.9, 9.3, 11.4, 5.8, 9.7, 8.8, 6.7, 13.2

Find the Mean and standard deviation and show work

Answer 1

The mean checkout time for the 12 customers is 8.65 minutes. To find the standard deviation, subtract the mean from each time to find the deviation, square it, sum them, divide by 11, and take the square root.

Step-by-step explanation:

To find the mean checkout time, we add up all the recorded times and divide by the number of customers. The sum of the checkout times is 4.6 + 8.5 + 6.1 + 7.8 + 10.9 + 9.3 + 11.4 + 5.8 + 9.7 + 8.8 + 6.7 + 13.2, which equals 103.8 minutes. Divided by 12 customers, the mean checkout time is 103.8 / 12 = 8.65 minutes.

To calculate the standard deviation, we follow these steps:

1. Subtract the mean from each individual checkout time to find the deviation for each time.
2. Square each deviation.
3. Sum all the squared deviations.
4. Divide the sum by the number of values minus one to find the variance. In this case, that's 11 since we have 12 values.
5. Take the square root of the variance to find the standard deviation.

Performing these calculations, we find the standard deviation for the checkout times.