Sampling > Sampling Variability

## What is sampling variability?

Sampling variability is **how much an estimate varies between samples**. “Variability” is another name for range; Variability between samples indicates the *range of values* differs between samples.

Sampling variability is often written in terms of a statistic. The variance (σ^{2}) and standard deviation (σ) are common measures of variability. You might also see reference to the variability of the sample mean (x&772;), which is just another way of saying the sample mean differs from sample to sample. **Sampling variability only refers to a statistic (i.e. a number generated from a sample) — never a population.**

## Variability and Sampling Error

A closely related term (almost a synonym) is sampling *error*. An *error *in sampling isn’t a mistake — it’s a measure of how much a value differs from the “true” value. Let’s say the true weight of a population is 150 lbs. You take a sample and find the mean weight for the sample is 151 lbs. The 1 lb difference is an “error.” If you sample again, you might get different mean weights of 148 lbs, or 150.5 lbs, or 153 lbs. The different errors — 1/2 lb, 1 lb, 2 lbs, 3 lbs — are a reflection of the variability between your samples, or **sampling variability.**

## Variability and Sample Sizes

Increasing or decreasing sample sizes leads to changes in the variability of samples. For example, a sample size of 10 people taken from the same population of 1,000 will very likely give you a very different result than a sample size of 100.

There is no “perfect” sample size that will give you accurate estimates for the sample mean, variance and other statistics. Instead, you take your best “guess” — using standardized statistical procedures (see: Finding the sample size). In general, estimates will change from sample to sample and will probably never exactly match the population parameter.

**Next**: Sampling Distributions.

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**Stephanie Glen**. "Sampling Variability: Definition" From

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