A certian company enjoyed 3.5% profits in year 1 over its revenue in Year 0. In Year 2, it enjoyed 5.75% profits over Year 1. In Year 3, it posted 1.25% profits over Year 2. What single, constant profit over this period of years would have produced the same profit? The teacher stated to use either harmonic or geometric mean, which ever is appropriate. I am not sure which one to use or how to set it up. My stats book is sadly lacking with examples of these.

Any direction would be helpful and much appreciated.

To find the single, constant profit over the period of years that would have produced the same profit, we can use the geometric mean. The geometric mean is appropriate here because we are dealing with percentages and looking for a constant rate over multiple periods.

Here's how you can set it up:

1. Start by converting the given percentages into decimal form. For example, 3.5% becomes 0.035, 5.75% becomes 0.0575, and 1.25% becomes 0.0125.

2. Next, add 1 to each of these decimal values to get the growth factors. For example, 0.035 + 1 = 1.035, 0.0575 + 1 = 1.0575, and 0.0125 + 1 = 1.0125.

3. Now, multiply all these growth factors together to find the overall growth factor over the period of years. In this case, it would be 1.035 * 1.0575 * 1.0125.

4. Finally, subtract 1 from the result obtained in step 3 to find the constant profit as a percentage. So, (1.035 * 1.0575 * 1.0125) - 1.

Solving this expression will give you the desired constant profit over the period of years.

Note that if you were asked to use the harmonic mean instead, you would instead calculate the harmonic mean of the growth factors. However, since the teacher specified to use the geometric mean, follow the steps outlined above.