Question

At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10 (10 being the highest rating) for several activities: promptness, record keeping, appearance, and bedside manner with patients.

Then an average is determined by giving a weight of 1 for promptness, 3 for record keeping, 4 for appearance, and 2 for bedside manner with patients. What is the average rating for a nurse with ratings of 6 for promptness, 4 for record keeping, 1 for appearance, and 2 for bedside manner? (Enter your answer to one decimal place.)

Answer 1

2.6

Explanation:

This is a "weighted average" problem, of course.

The idea is that you first multiply each rating by its weight, then you add all those up.

Then you divide by the sum of the weightings.

Easier to see using the specific numbers given:

1·6 + 3·4 + 4·1 + 2·2

See what I did there? The first number is the weight of each category, then it's multiplied by the rating the nurse got in that area.

That simplifies to:

6 + 12 + 4 + 4 = 26

And that's the sum we're going to divide by something, just like any other average. But what do we divide by? We add up all the weightings and divide by that:

1 + 3 + 4 + 2 = 10

So now we divide sort of the raw score by the sum of the weights:

26/10 = 2.6

This nurse got an overall rating of 2.6.

There are tons of examples of this on the web if you want more practice.