A sample of the personnel files of eight male employees revealed that, during a six month period, they lost the following number of days due to illness: 2, 0, 6, 3, 10, 4, 1, and 2.

Caluculate the mean deviation.

First, calculate the mean (average) number days lost. The deviation, for any observation, is the difference between the observed value and the mean.

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To calculate the mean deviation, follow these steps:

1. Calculate the mean (average) of the data set by adding up all the values and dividing by the number of values. In this case, you have 8 values:
(2 + 0 + 6 + 3 + 10 + 4 + 1 + 2) / 8 = 28 / 8 = 3.5

2. Subtract the mean from each value in the data set, then take the absolute value (ignore the negative signs). This will give you the deviation of each value from the mean. The deviations for this data set would be:
|2 - 3.5| = 1.5
|0 - 3.5| = 3.5
|6 - 3.5| = 2.5
|3 - 3.5| = 0.5
|10 - 3.5| = 6.5
|4 - 3.5| = 0.5
|1 - 3.5| = 2.5
|2 - 3.5| = 1.5

3. Calculate the mean of the absolute deviations by adding up all the deviations and dividing by the number of values. In this case, you have 8 deviations:
(1.5 + 3.5 + 2.5 + 0.5 + 6.5 + 0.5 + 2.5 + 1.5) / 8 = 18.5 / 8 = 2.3125

So, the mean deviation for this data set is 2.3125.