Eyeball Estimation

Eyeball estimation refers to inspecting data and quickly making an educated guess about the approximate magnitude of relevant statistics without using a calculator or statistical tables.

Here are some examples:

• To eyeball estimate the mean from data presented as a histogram, imagine that the histogram is cut out of plywood. The mean of the distribution is the point where that piece of plywood would balance.
• To eyeball estimate the mean from data presented in a table, find the largest and the smallest values; the mean will be approximately halfway between those values. For example, if the values of X are 7, 8, 6, 7, 5, 6, 4, 7, 6, 8, 9, 7, 8, 9, 7, 6, 6, 7, 4, 5, 6, 5, 4, 8, 7, the largest value is 9 and the smallest value is 4; the mean will be approximately 6.5. (It is actually 6.48.)
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• To eyeball estimate the standard deviation from data presented as a histogram, superimpose a sketch of a normal distribution over the histogram—make the normal distribution cut through the tops of some of the histogram's bars. The standard deviation will be approximately the distance from the mean to the inflection point of the normal distribution.
• To eyeball estimate the standard deviation from data presented in a table, find the range (the largest value minus the smallest value). The standard deviation is roughly a quarter of the range. For example, for the data above, the largest value is 9 and the smallest value is 4, so the range is 9 – 4 = 5. The standard deviation will be approximately 5/4, or 1.25. (It is actually 1.45.)

The other commonly used descriptive statistics (correlation coefficients, regression constants, areas under normal distributions) can also be eyeball estimated, as can straightforward inferential statistics such as t tests and analyses of variance.

Eyeball estimation is not a substitute for accurate computation. Eyeball estimates are “in-the-ballpark” approximations that can be affected (sometimes dramatically) by such factors as skew. However, eyeball estimation is a valuable skill. It enables the observer to get a sense of the data and to spot mistakes in the computations.

Students benefit from eyeball estimation because it cultivates genuine understanding of statistical concepts. The ability to make an in-the-ballpark, educated guess is better evidence of comprehension than is the ability to compute an exact result from a formula. Furthermore, eyeball estimation is quick. A beginning student can eyeball estimate a standard deviation in about 15 seconds; computation would take the same student about 15 minutes. Furthermore, while students are eyeball estimating standard deviations, they are developing their comprehension of the standard deviation as a measure of the width of a distribution. By contrast, almost no time involved in the computation of a standard deviation is focused on that comprehension.