# Troublesome coefficient of variation question

1. Nov 27, 2009

### th_05

Given the following data for three possibile investments, A, B and C, calculate the coefficient of variation and with the aid of a diagram explain which is the least risky investment.

Expected Profit: A - 100 B - 120 C - 140
Standard Devi.: A - 10 B - 30 C - 20

I presume to calculate the COV you divide the standard deviation by the mean, to give you:

A: 100/10 = 0.1 B: 30/120 = 0.25 C: 20/140 = 0.14

I am struggling with how/what sort of diagram to use and how to explain which is the least risky investment. Any ideas would be great.

2. Nov 27, 2009

### Staff: Mentor

In your first calculation for COV, you have 100/10 and you should probably have 10/100.

Neither of the statistics books I have has a definition for coefficient of variation, so that's a new one on me.

Something that might be helpful is that in a normal distribution, about 69% of the values fall within one standard deviation of the mean. If the profits in these investments are normally distributed, then for investment A, we would expect that 69% of the time the profit would be between $90 and$110. If you look at each of the other investments in a similar manner you'll get a range of possible profits for each, so maybe you can determine the relative risk in this way.