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.
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
∴ Standard deviation