Question

If $\overline{X}$ is the mean of the ten natural numbers x₁, x₂, x₃,..., x₁₀, show that
$(x_1-\overline{X})+(x_2-\overline{X})+...+(x_{10}-\overline{X})=0$.

Answer 1

Ifbe the mean of the n observations, then we have

Given thatis the mean of the 10 natural numbers. So, we have

We have to show that

That is to show that the sum of the deviations of the 10 natural numbers from their mean is 0.

We have

Hence the proof is complete.