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Question
The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is
Options
`k bar(X) `
`bar(X)/k`
`bar(X) +k`
`bar(X)- k`
Solution
Let us take n observations `X_i,...,X_n.`
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)^n X_i = n bar(X)`
Multiply a constant k to each of the observations. Then the observations becomes `kX_i,...,kX_n.`
If `bar(Y)` be the mean of the new observations, then we have
`bar(Y) = 1/n sum _(i=1)^n kX_i`
`= k/n sum _(i=1)^n X_i`
`= k . 1/n sum _(i=1)^n X_i`
`= kbar(X)`
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