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Using range to estimate SD (σ)

This provides a quick and simple estimate of standard deviation. Providing your data approximate to a normal distribution, their population standard deviation (σ) can be estimated from the range.

Algebraically speaking -

σ =   Range multiplier(n)

where :

  • σ is the estimated standard deviation,
  • the range is the maximum - minimum
  • the multiplier(n) is looked up in the appropriate table for that number of observations.

Table 1 gives the values of the multiplier for n = 1 to 1000.

Let's work this out for our lamb PCVs

Worked example

Lamb No.PCV
133
226
329
432
531
Range33-26 = 7

We will assume the data follow a normal distribution.

The range estimate of the standard deviation (σ) is therefore:

Range Estimate of σ    =    Multipliern=7 Range
     =    2.59

Τhis compares with a value of 2.95 using the corrected average of the sum of the squared deviations from the mean.

The range estimate provides a quick and easy way to check the standard deviation when calculated in the conventional way.

For small sample sizes (n<10) the range estimator is surprisingly efficient (>85%). Efficiency in this sense means that to get the same accuracy for s calculated when n=10, we would have to use a sample size of 12 for the range estimator. Hence the efficiency is approximately 10/12 or 85%.