Question

The mean of a data set is 124. The mean absolute deviation is 38. What is the greatest possible number within the mean absolute deviation?

Answer 1

Infinity

Explanation:

The given parameters are;

The mean of the data, μ = 124

The mean absolute deviation = 38

The mean absolute deviation is given as follows;

`Mean \ absolute \ deviation = (\sum \left | X - \mu \right |)/(N) = 38`

Where;

μ = Mean

X = Score

N = The number of scores

Therefore;

`N * 38 = \sum\limits_(i = 1)^N \left | X - \mu \right |} = \sum\limits_(i = 1)^N \left | X -124 \right |}`

When there are an infinite number of terms, N = ∞, the greatest possible number within the mean absolute deviation is therefore also infinite

`\infty * 38 = \sum\limits_(i = 1)^(\infty) \left | X - \mu \right |} = \infty`

`Greatest \ possible \ value \ for \left | X - \mu \right |} = \infty`