Question

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows:

5, 2, 8, 2, 3, 2, 4, 12
The variance for this distribution is Assume sample data.
A) 33.75
B) 11.19
C) 12.79
D) 15.75

Answer 1

The variance for the given distribution is 12.75.

Step-by-step explanation:

To find the variance for the given distribution, we need to follow these steps:

1. Calculate the mean of the scores.
2. Find the difference between each score and the mean.
3. Square each difference.
4. Find the sum of all the squared differences.
5. Divide the sum by the number of observations.

Let's calculate the variance:

Mean = (5 + 2 + 8 + 2 + 3 + 2 + 4 + 12) / 8 = 6

Differences from the Mean:

(5 - 6) = -1

(2 - 6) = -4

(8 - 6) = 2

(2 - 6) = -4

(3 - 6) = -3

(2 - 6) = -4

(4 - 6) = -2

(12 - 6) = 6

Squared Differences:

1, 16, 4, 16, 9, 16, 4, 36

Sum of Squared Differences: 1 + 16 + 4 + 16 + 9 + 16 + 4 + 36 = 102

Divide the sum by the number of observations: 102 / 8 = 12.75

Therefore, the variance for this distribution is 12.75 (rounded to two decimal places).