The tutor offers a case study in statistics.

Around here, forestry might be the leading industry.  Of course, I hardly ever see evidence of it; up in the hills is where the work is done.

As I understand, one angle of the forest industry is trading woodlots. The buyer may not harvest the wood, but rather hold it until a good time to sell. The key in such a market is understanding the value of the trees on a given lot – which, largely, can boil down to statistics.

Case 1:

Let’s imagine Bill owns Managed Woodlot A. Nine years ago he knew the mean tree height was 25m, with standard deviation 8m. Let’s imagine a mature tree commonly grows about 3% per year (likely fairly reasonable, considering my post here).

Bill wonders, has the standard deviation of the trees’ heights necessarily changed, given the growth? (The reader might want a briefing on mean and standard deviation; see my post here.)

Solution:

First, we realize the effect on a given tree’s height, x_i, of nine years’ growth at 3% per year:

x_i*(1.03)^9 ≈ 1.3x_i

We can assume the same effect on the mean x

Σ1.3x_i/n = 1.3x

Using the standard deviation formula

s=(Σ(x_i–x)^2/(n-1))^0.5

we substitute the grown values:

s=(Σ(1.3x_i-1.3x)^2/(n-1))^0.5

We can factor out 1.3:

s=(Σ1.3^2(x_i–x)^2/(n-1))^0.5

to finally arrive at

s=1.3(Σ(x_i–x)^2/(n-1))^0.5

We see that, indeed, the standard deviation of the trees’ heights has changed: like the mean height, it’s also 1.3 times what it was nine years ago.

Bill can proceed to other reasonable conclusions from the results here. I’ll be telling about them in future posts:)

Source:

Levin, Richard I. Statistics for Management. Englewood Cliffs, New Jersey: Prentice-Hall, 1978.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.