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 |
| 1 | 33 |
| 2 | 26 |
| 3 | 29 |
| 4 | 32 |
| 5 | 31 |
| Range | 33-26 = 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%.
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