Question

# The mean square deviations of a set of observations x1, x2, ⋯, xn about a point c is defined to be 1n∑ni=1(xi−c)2 The mean square deviations about -1 and +1 of a set of observations are 7 and 3, respectively. Find the standard deviation of this set of observations.

A

3

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B
3
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C
5
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D
5
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Solution

## The correct option is A √3 Mean square deviations,=1n∑ni=1(xi−c)2 about c. Also, given that mean square deviation about – 1 and + 1 are 7 and 3, respectively. ⇒1n∑ni=1(xi+1)2=7 and 1n∑ni=1(xi−1)2=3⇒ ∑ni=1x2i+2∑ni=1xi+n=7nand ∑ni=1x2i−2∑ni=1xi+n=3n⇒∑ni=1x2i+2∑ni=1xi=6n and ∑ni=1x2i−2∑ni=1xi=2n ⇒∑ni=1xi=n⇒¯x=∑ni=1xin=1 ∴ Standard deviation =√1n∑ni=1(xi−¯x)2=√1n∑ni=1(xi−1)2=√3

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