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. What is the mean deviation (in days)?
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A. B. C. D. E.Explanation
The mean is 3.5. The mean deviation is the absolute values of the deviation from the mean. (1.5 + 3.5 + 2.5 + 0.5 + 6.5 + 0.5 + 2.5 + 1.5)/8 = 19/8 = 2.375
To calculate the mean deviation, we need to follow these steps:
Step 1: Calculate the mean (average) of the data set. Step 2: Subtract the mean from each data point. Step 3: Take the absolute value of each result. Step 4: Calculate the mean of the absolute deviations.
Let's apply these steps to the given data set of the number of days lost due to illness: 2, 0, 6, 3, 10, 4, 1, and 2.
Step 1: Calculate the mean: Mean = (2 + 0 + 6 + 3 + 10 + 4 + 1 + 2) / 8 = 28 / 8 = 3.5
Step 2: Subtract the mean from each data point: 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
Step 3: Take the absolute value of each result: |-1.5| = 1.5 |-3.5| = 3.5 |2.5| = 2.5 |-0.5| = 0.5 |6.5| = 6.5 |0.5| = 0.5 |-2.5| = 2.5 |-1.5| = 1.5
Step 4: Calculate the mean of the absolute deviations: Mean Deviation = (1.5 + 3.5 + 2.5 + 0.5 + 6.5 + 0.5 + 2.5 + 1.5) / 8 = 18 / 8 = 2.25
The mean deviation is 2.25 days.
None of the provided answer options (A, B, C, D, E) match the calculated mean deviation of 2.25 days.