Question

The mean of n observations is X. If k is added to each observation, then the new mean is

पर्याय

• X

•  X + k

•  X − k

• kX

Answer 1

Let us take n observations X₁.,....,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)^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).