Question

Durations of sunshine (in hours) in Amritsar to first 10 days of August 1997 as reported by the Meteorological Department are given below:
9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9

(i) Find the mean X.

(ii) Verify that $\sum _{i=1}^{10}(x_i-\overline{X})=0$

Answer 1

Given that the durations of sunshine (in hours) in Amritsar for 10 days are 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, and 10.9.

(i) We have to find their mean.

Remember the definition of mean of n values x₁, x₂… x_n is

Therefore the mean duration of sunshine is

(ii) We have to prove that

We have

Hence the proof is complete.