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Question
The mean of n observations is X. If k is added to each observation, then the new mean is
Options
X
X + k
X − k
kX
Solution
Let us take n observations X1.,....,Xn.
If `bar(X) `be the mean of the n observations, then we have
`bar(X) = 1/n sum_(i=1)^n X_i`
`⇒ sum_(i=1)^nX_i = nbar(X)`
Add a constant k to each of the observations. Then the observations becomes `X_i+k,...,X_n+k`
If `bar(Y) `be the mean of the new observations, then we have
`bar(Y) = 1/n sum_(i=1)^n(X_i+k)`
=`1/nsum _(i=1)^n X_i + 1/n sum_(i=1) ^n k `
`= bar(X) +1/n. nk `
`= bar(X) + k `
Hence, the correct choice is (b).
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