What is a 'Sampling Distribution'

A sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

BREAKING DOWN 'Sampling Distribution'

A lot of data drawn and used by academicians, statisticians, researchers, marketers, analysts, etc. are actually samples, not population. A sample is a subset of a population. For example, a medical researcher that wanted to compare the average weight of all babies born in North America from 1995 to 2005 to those born in South America within the same time period cannot within a reasonable amount of time draw the data for the entire population of over a million childbirths that occurred over the ten-year time frame. He will instead only use the weight of, say 100 babies, in each continent to make a conclusion. The weight of 200 babies used is the sample and the average weight calculated is the sample mean.

Now suppose that instead of taking just one sample of 100 newborn weights from each continent, the medical researcher takes repeated random samples from the general population, and computes the sample mean for each sample group. So, for North America, he pulls up data for 100 newborn weights recorded in the US, Canada, and Mexico as follows: four 100 samples from select hospitals in the US, five 70 samples from Canada, and three 150 records from Mexico, for a total of 1200 weights of newborn babies grouped in 12 sets. He also collects a sample data of 100 birth weights from each of the 12 countries in South America. Each sample has its own sample mean and the distribution of the sample means is known as the sample distribution.

The average weight computed for each of the 2400 sample set is the sampling distribution of the mean. Not just the mean can be calculated from a sample. Other statistics, such as the standard deviation, variance, proportion, and range can be calculated from a sample data. The standard deviation and variance measure the variability of the sampling distribution. The number of observations in a population, number of observations in a sample, and the procedure used to draw the sample sets determine the variability of a sampling distribution. The standard deviation of a sampling distribution is called the standard error. While the mean of a sampling distribution is equal to the mean of the population, the standard error depends on the standard deviation of the population, the size of the population, and the size of the sample. Knowing how spread apart the mean of each of the sample sets are from each other and from the population mean will give an indication of how close the sample mean is to the population mean. The standard error of the sampling distribution decreases as the sample size increases.

Normal Distribution and Shape

A population or one sample set of numbers will have a normal distribution. However, because a sampling distribution includes multiple sets of observations, it will not necessarily have a bell-curved shape. Following our example, the population average weight of babies in North America and in South America has a normal distribution because some babies will be underweight (below the mean) or overweight (above the mean), with most babies falling in between (around the mean). If the average weight of newborns in North America is seven pounds, the sample mean weight in each of the 12 sets of sample observations recorded for North America will be close to seven pounds as well. But if you graph each of the averages calculated in each of the 1200 sample groups, the resulting shape may result in a uniform distribution, but it is difficult to predict with certainty what the actual shape will turn out to be. The more samples the researcher uses from the population of over a million weight figures, the more the graph will start forming a normal distribution.

  1. Sample

    A sample is a smaller, manageable version of a larger group. ...
  2. Systematic Sampling

    Systematic sampling is a probability sampling method in which ...
  3. Sample Size Neglect

    Sample size neglect occurs when an individual infers too much ...
  4. Simple Random Sample

    A subset of a statistical population in which each member of ...
  5. Attribute Sampling

    Attribute sampling is a statistical method typically used in ...
  6. Sampling Error

    A statistical error to which an analyst exposes a model simply ...
Related Articles
  1. Investing

    How to Use Stratified Random Sampling

    Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroup’s ...
  2. Investing

    Hypothesis testing in finance: Concept and examples

    When you're indecisive about an investment, the best way to keep a cool head might be test various hypotheses using the most relevant statistics.
  3. Investing

    How Vanguard Index Funds Work

    Learn how Vanguard index funds work. See how the index sampling technique allows Vanguard to charge low expense ratios that can save investors money.
  4. Investing

    Find the right fit with probability distributions

    Discover a few of the most popular probability distributions and how to calculate them.
  5. Investing

    Optimize your portfolio using normal distribution

    Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
  6. Insights

    These Companies Are Poised for Growth as Global Population Growth Comes Online

    While there are many concerns about population growth putting pressure on natural resources such as water and energy, these increased demands can spell profits for certain companies that can ...
  7. Personal Finance

    Common Interview Questions for Accountants

    Learn which job interview questions to prepare for to help advance your accounting career. Discover that what you do not say is as important as what you do say.
  8. Financial Advisor

    How to Save Clients from RMD Aggregation Mistakes

    Advisors can help clients avoid required minimum distribution mistakes in their retirement plans.
  1. What's the difference between a representative sample and a random sample?

    Explore the differences between representative samples and random samples, and discover how they are often used in tandem ... Read Answer >>
  2. What are the benefits of financial sampling?

    Learn more about how financial sampling is used to determine whether or not inaccurate or fraudulent information exists in ... Read Answer >>
  3. How do I calculate the standard error using Matlab?

    Learn how to calculate the standard error for a sample statistical measure, such as the sample mean, using standard Matlab ... Read Answer >>
  4. What Are Stratified Random Sampling's Pros & Cons?

    Stratified random sampling provides a more accurate sampling of a population, but can be disadvantageous when researchers ... Read Answer >>
  5. What is a relative standard error?

    Find out how to distinguish between mean, standard deviation, standard error and relative standard error in statistical survey ... Read Answer >>
Hot Definitions
  1. Working Capital

    Working capital, also known as net working capital is a measure of a company's liquidity and operational efficiency.
  2. Bond

    A bond is a fixed income investment in which an investor loans money to an entity (corporate or governmental) that borrows ...
  3. Compound Annual Growth Rate - CAGR

    The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer ...
  4. Net Present Value - NPV

    Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...
  5. Price-Earnings Ratio - P/E Ratio

    The Price-to-Earnings Ratio or P/E ratio is a ratio for valuing a company that measures its current share price relative ...
  6. Internal Rate of Return - IRR

    Internal Rate of Return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments.
Trading Center