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Statistical Thinking for Industrial Problem Solving
We estimate the standard deviation of sample means, or the standard error, by dividing the sample standard deviation by the square root of the sample size.
This tells us that the spread of the distribution of sample means becomes smaller by a factor of Root(n) as the sample size increases.
This explains why we often use sample averages in statistics.
- We get more precise estimates of population behavior by taking samples. Larger samples give more precise estimates than smaller samples.
- The standard deviation of the sample mean, or the standard error, is always less than the standard deviation of the raw data (by a factor of the square root of the sample size).
- And sample averages are approximately normally distributed, even if the underlying distribution is not normal, and as the sample size increases, this distribution becomes more normal.
Averaging is also an effective noise filter, enabling you to focus in and see the signal through the noise of the variability in the raw data.
You’ll see evidence of the Central Limit Theorem at work in in the Quality Methods module, and again when you learn about statistical intervals and hypothesis tests in the Decision Making with Data module.
In the next practice exercise, you explore the Central Limit Theorem using the Sampling Distribution of Sample Means teaching module.
