Question

A handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue. The company would like to position a new office between the two cities using weighted averages based on the typical number of calls received from each city. If Jonesville has a weight of 3 and Bellevue has a weight of 5, how far from Bellevue should the office be located?

Answer 1

The new office should be at a distance of 37.5 miles from Jonesville.

The weighted mean is the sum of all elements in a data-set multiplied by their weights, divided by the sum of the weights. For example, if x1 and x2 are the elements with weights w1 and w2 respectively, then the weighted average is calculated using the given formula-

M =  {(x1*w1) + (x2*w2)}/ (w1+w2)

Here, we are given that two cities Jonesville and Bellevue, 60 miles apart.

Let Jonesville be at point 0 and Bellevue be at point 60.

Jonesville has a weight of 3 and Bellevue has a weight of 5.

Thus, the weighted average can be calculated as follows-

Mean = {(60*5) + (0*3)}/8

= 300/8

= 75/2

= 37.5

Thus, the new office should be at a distance of 37.5 miles from Jonesville.

Learn more about weighted averages here-

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