Question

Calculate the average value of the numbers 3, 3, 5, 5 first by calculating the normal average and then by calculating the weighted average. Are the two results the same?

Answer 1

Given numbers are 3, 3, 5, 5 total we have 4 numbers

a] normal average = ( 3 + 3 + 5 + 5 ) / 4 = 16 / 4 = 4

b] weighted average, in which we first allocate the weights for each values and here weights are 0.25 for all given numbers

weighted average = (3 * 0.25 + 3 * 0.25 + 5 * 0.25 + 5 * 0.25) / (Sum of weights)

                          = (3 * 0.25 + 3 * 0.25 + 5 * 0.25 + 5 * 0.25) / ( 0.25 + 0.25 + 0.25 + 0.25 )

                          = 0.25 * ( 3 + 3 + 5 + 5 ) = 0.25 * 16 = 4

We notice that both normal average and weighted average are same