The central limit theorem says the distribution of sample means approaches normal as the sample size grows, with a standard deviation equal to sigma divided by the square root of n. For moderately skewed data, subgroups of 4 or 5 are already close enough, which is why X-bar charts tolerate non-normal data while individuals charts do not. It also explains why averaging 4 readings halves the noise of a measurement.
Thickness per site is skewed, but the wafer mean of nine sites is close to normal. Central limit theorem does the work.
Also heard as
- CLT
Related terms
Normal distribution
Symmetric bell-shaped distribution set by a mean and a standard deviation, the default model for measurement data.
X-bar and R chart
Paired control charts for subgroup averages and subgroup ranges, the workhorse for measured data sampled in small groups.
I-MR chart
Individuals and moving range chart: the control chart for one measurement per period, such as one batch or one lot.
Standard deviation
Typical distance of individual values from their mean, the basic measure of spread, written as sigma or s.