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The Laws of Averages

Letter from Neil Seitz

School election article – December 2001 – Colorado Central Magazine


First the good news. I have thoroughly read and enjoyed your magazine for many years. I find myself very much connected with your articles from my background of planning commission, hot springs, schools and land trust in Saguache County. Someday I hope to see an article about the aspect of growth that concerns just the sheer number of people without regard to wealth, houses etc. You might say a Planned Parenthood approach.

Speaking of numbers, now the bad news. Let me throw in a few quotes; the first is my favorite:

There are three kinds of lies: lies, damned lies and statistics.

Benjamin Disraeli (1804-81), English statesman, author. Quoted in: Mark Twain, Autobiography, ch. 29 (ed. by Charles Neider, 1959).

He uses statistics as a drunken man uses lamp-posts for support rather than illumination.

Andrew Lang (1844 1912), Scottish author. Quoted in: Alan L. Mackay, The Harvest of a Quiet Eye (1977).

In the “How Does It Add Up?” in the November editiion you allowed (as temporary mentor of Annie) a very common mathematical error. On page 15, the sentences “…average teacher salary for the ten districts…”, “…percent of its funds on teacher salaries…district average…” and “…average number of days missed for the ten districts…” all used an average of averages. This can be very misleading if the group of averages widely differ and are based on varied number of samples. In one of your examples below, the true average, if I did my late night calculations correctly, is not much different from yours.

District Teachers Average Salary Total (Tchrs x Av. Sal)

Buena Vista 69.5 $31,975 $2,222,262

Cotopaxi 29.1 30,847 897,647

Custer County 32.7 30,899 1,010,397

Florence 115.0 37,402 4,301,230

Gunnison 122.9 31,980 3,930,342

Lake County 75.0 31,701 2,377,575

Moffat 27.0 27,486 742,122

Mtn Valley 21.3 2 9,557 629,564

South Park 51.7 26,386 1,364,156

Salida 68.5 34,507 2,363,729

TOTALS 612.7 312,740 19,839,018

Your “average” salary was $312,740 / 10 schools = $31,274

The true average is $19,839,018 / 612.7 teachers = $32,380

The difference between the “averages” would grow if all the small schools salaries were on one end of the scale and all the large schools were on the other. Try the average salary of Moffat and Florence districts.

I didn’t take the time on percent of budget on salaries or percent of days absent but the same rule holds.

Neil Seitz

Valley View Hot Springs

Orient Land Trust