# The algebraic sum of the deviations of a set of n values from their mean is - Mathematics

MCQ

The algebraic sum of the deviations of a set of n values from their mean is

• 0

• n − 1

•  n

• n + 1

#### Solution

If bar( X) be the mean of the observations q X_i,...,X_n, then we have

bar(X) = 1/nsum_(i=1)^n X_i

⇒ sum_(i=1)^n X_i = nbar(X)

Let  bar(X) be the mean of n values X_i,...,X_n . So, we have

bar(X) = 1/nsum_(i=1)^n X_i

⇒ sum_(i=1)^n X_i = nbar(X)

The sum of the deviations of n values X_i,...,X_n from their meanbar(X) is

(x_1 - bar(X) ) +(x_2 - bar(X) )+......+(x_n-bar(X))

= sum_(i=1)^n(x_i- bar(X))

= sum_(i=1)^n x_i- sum_(i=1)^n  bar(X)

= nbar(X) - nbar(X)

=0

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 24 Measures of Central Tendency
Q 12 | Page 22