Scales of Measurement:

Introductory quotes:
"Attributing to statistics the inherent ability to describe universal laws leads to many prevalent and interesting fallacies. Following G.K. Chesterton, we caution against using statistics as a drunk uses a lamp post: for support rather than illumination." (A. Einstein, 1956)

"There are three kinds of lies: lies, damn lies, and statistics." (Benjamin Disraeli, the prime minister of the British Empire from 1874-1880)

  1. Geologists have a "hardness" scale for rocks 1-10
  2. Three cubes were measures with a ruler and found to have volumes of 40, 65, and 75 cubic inches
  3. Three different highways are identified by their numbers: 95, 76, 476
  4. Republicans, Democrats, Independents, Libertatians
  5. The pages of a book 1-150.

Statistics with Scales:

Nominal: Mode

Ordinal: Median or Mode

Interval/Ratio: Mean Median or Mode

Descriptive Statistics

Mean= average

Median= point at which 1/2 scores fall above, 1/2 below
12, 11, 10, 9, 8
45, 44, 43, 42, 41, 40
10, 9, 8, 8, 8, 7, 7

Mode= middle point

Standard Deviation variability from Mean

Why is this important?

Even with interval/ratio data, the mean may give inaccurate data.

Example: Swampy Acres Retirement Site

The developer of SARH is attempting to sell lots in a "Southern Paradise" to northern buyers. The "marks" express concern that flooding might occur. The developer reassures them by explaining that the average elevation of the lots is 78.5 feet and that the water has never exceeded 25 feet.

So, would you buy a new lot from this developer?

Frequency distribution of Lot Elevations at SARH
Elevation on feetNumber of lotsFx

Mean elevation = 78.5 (20 lots above water)
Median Elevation = 12.5

Mean larger than median = "skew"