What is the range of 1 standard deviation?

What is the range of 1 standard deviation?

When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value.

The standard deviation is approximately equal to the range of the data divided by 4. Thats it, simple.

Find the largest value, the maximum and subtract the smallest value, the minimum, to find the range. Then divide the range by four.

Example

Say you have the following measurements:

9, 13, 14, 17, 18, 21, 22, 25, 29, and 35

Which has a mean of 20.3, sample standard deviation of 7.8 and population standard deviation of 7.4.

The maximum value is 35 and the minimum value is 9.

35 9 = 26.

26 divided by 4 is 6.5.

About the best you can say is that 6.5 is in the ball part of 7.4 and 7.8 its a rough estimate at best.

How it works

Consider the normal distribution for a moment. 95% of the data is within plus or minus two standard deviations.

For a relatively small sample, the range is likely to based on data from within this 95% range. The range of the two standard deviations is the full range of the data from the distribution, so a relatively small sample will most likely contain data inside this range. Thus the range rule provides a rough estimate, often a bit smaller than the actual standard deviation.

Even for distributions that are not normally distributed the bulk of the data will be within the plus or minus two standard deviations, so it should provide a rough estimate of most any distribution.

A quick trick to help you make sense of data.


Related:

Variance(article)

Root Sum Squared Tolerance Analysis Method(article)

Point and Interval Estimates(article)