Let xi(1≤i≤10) be ten observations of a random variable  X. If ∑i=110 xi−p=3 and ∑i=110 xi−p2=9, where0≠p∈R, then the standard deviation of these observations is

Let xi(1i10) be ten observations of a random variable  X. If i=110xip=3 and i=110xip2=9, where

0pR, then the standard deviation of these observations is

  1. A

    45

  2. B

    35

  3. C

    910

  4. D

    710

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    Solution:

    Let σX be the standard deviation. Then,

    σX2=110Σxip2110Σxip2=9103102=81100 σx=910

    It follows from the above discussion that in case of individual observations, variance/ standard deviation may be computed by applying any of the above three formulas. In order to calculate the variance when deviations are taken from the actual mean, we may use the following algorithm.

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