 Quandaries and Queries

My husband and I are not math people, but have a math question. Perhaps you can help.

He's doing performance reviews at work.

The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year.

The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year.

How do I solve for the other performance review numbers.

They are:

4.15
3.8
2.7
4.05
3.9
3.4
4.9
4.45

Thanks for any insight you might be able to give me.

Lara

Hi Lara,

As stated there is not enough information. I'm going to assume that there is what we call a linear relationship between the score and the % reward. In other words it is a straight line graph. Such graphs have the form y = mx + b; in your case the y is the raise and the x is the score on the performance review. The two pieces of info you gave tell us that

3.5 = 3.92m + b and
6.0 = 4.9m + b
If we solve these 2 equations in the two unknowns m and b you find, roughly, that y = 2.55x - 6.5 (you could approximate this by y = 2.5(score) - 6.5) Thus if you let x = 4.9 you get y = 2.55(4.9) - 6.5 = 6.0%. In all you'll find the corresponding numbers as follows
Score %
4.9 6.00
3.92 3.50
4.15 4.08
3.8 3.19
2.7 0.39
4.05 3.83
3.9 3.45
3.4 2.17
4.9 6.00
4.45 4.85

Hope this helps,
Penny

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