What is a Sampling Distribution?

A sampling distribution is a graph of a statistic for your sample data. While, technically, you could choose any statistic to paint a picture, some common ones you’ll come across are:

Mean absolute value of the deviation from the meanVariance of the sample

Up until this point in statistics, you’ve probably been plotting graphs for a set of numbers. For example, you might have graphed a data set and found it follows the shape of a normal distribution with a mean score of 100. Where probability distributions differ is that you aren’t working with a single set of numbers; you’re dealing with multiple statistics for multiple sets of numbers. If you find that concept hard to grasp: you aren’t alone.

While most people can imagine what the graph of a set of numbers looks like, it’s much more difficult to imagine what stacks of, say, averages look like.

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A Binomial Distribution is related to Mean of Sampling Distribution of the Proportion.

Proportions are something you probably already know. For example: 100 people are asked if they are democrat. If 50 people respond “yes” then the sample proportion p = 50/100. Technically (the “mathy way”): A sample proportion is where a random sample of objects n is taken from a population P; if x objects have a certain characteristic then the sample proportion “p” is: p = x/n.

The sampling distribution of a proportion is when you repeat your survey or poll for all possible samples of the population. For example: instead of polling asking 1000 cat owners what cat food their pet prefers, you could repeat your poll multiple times.

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Mean of Sampling Distribution of the Proportion

If a random sample of n observations is taken from a binomial population with parameter p, the sampling distribution (i.e. all possible samples taken from the population) will have a mean up=p. With a large sample, the sampling distribution of a proportion will have an approximate normal distribution.

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Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.Levine, D. (2014). Even You Can Learn Statistics and Analytics: An Easy to Understand Guide to Statistics and Analytics 3rd Edition. Pearson FT Press

CITE THIS AS:Stephanie Glen. "Sampling Distribution: Definition, Types, Examples" From Elementary Statistics for the rest of us!

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