Test Index

Measures of Central Tendency and Dispersion

Question : 103 of 211

Marks: +1, -0

Sum of the deviations about mean is :

Solution:

Concept:

The sum of deviations of all data points from the arithmetic mean is always zero.

Explanation:

Let the data be

x_1, x_2, \ldots, x_n

with mean

\bar{x}

The deviation of each value is

x_i - \bar{x}

Sum of deviations:

\sum (x_i - \bar{x}) = \sum x_i - n\bar{x}

Since

\bar{x} = \frac{\sum x_i}{n}

, we have

n\bar{x} = \sum x_i

Thus

\sum (x_i - \bar{x}) = 0

Answer:

Zero

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