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Question

Difficulty: EasyMeasures of Dispersion

What is the mean deviation of the data set 4,7,8,11,154, 7, 8, 11, 15?

Answer: 3.2

Answer

The mean deviation of the data set is 3.2.
To find the mean deviation, first calculate the mean of the dataset, which is 9. Then, compute the absolute difference of each number from 9, obtaining values of 5, 2, 1, 2, and 6. Finally, divide the sum of these absolute values (16) by the total number of items (5) to get 3.2.

Step-by-Step Solution

1
Calculate the arithmetic mean of the given data set.
The mean xˉ=9\bar{x} = 9.
The mean is needed to evaluate how far each data point deviates from the central value.
2
Find the absolute difference between each value and the mean.
The absolute deviations are 5, 2, 1, 2, and 6.
Mean deviation measures dispersion using absolute distances, ignoring negative signs.
3
Calculate the mean of the absolute deviations.
Mean deviation = 3.2.
Dividing the total sum of absolute deviations (16) by the number of observations (5) gives the mean deviation.

Key Concept

Mean Deviation for Ungrouped Data
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Topics

Measures of Dispersion

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