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

Answer:

Infinity

Step-by-step 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;

$Mean \ absolute \ deviation = \dfrac{\sum \left | X - \mu \right |}{N} = 38$

Where;

μ = Mean

X = Score

N = The number of scores

Therefore;

$N \times 38 = \sum\limits_{i = 1}^N \left | X - \mu \right |} = \sum\limits_{i = 1}^N \left | X -124 \right |}$

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

$\infty \times 38 = \sum\limits_{i = 1}^{\infty} \left | X - \mu \right |} = \infty$

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