how sampling distributions work
data allows statisticians researchers marketers analysts and academics to make important conclusions about specific topics and information it can help businesses make decisions about their future and boost their performance or it can help governments plan for services needed by a group of people a lot of data drawn and used are actually samples rather than populations a sample is a subset of a population put simply a sample is a smaller part of a larger group as such this smaller portion is meant to be representative of the population as a whole sampling distributions or the distribution of data are statistical metrics that determine whether an event or certain outcome will take place this distribution depends on a few different factors including the sample size the sampling process involved and the population as a whole there are a few steps involved with sampling distribution these include once the information is gathered plotted and analyzed researchers can make inferences and conclusions this can help them make decisions about what to expect in the future for instance governments may be able to invest in infrastructure projects based on the needs of a certain community or a company may decide to proceed with a new business venture if the sampling distribution suggests a positive outcome each sample has its own sample mean and the distribution of the sample means is known as the sample distribution special considerationsthe number of observations in a population the 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 1knowing 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 determining a sampling distributionlet s say a medical researcher wants to compare the average weight of all babies born in north america from 1995 to 2005 to those from south america within the same time period since they cannot draw the data for the entire population within a reasonable amount of time they would only use 100 babies in each continent to make a conclusion the data used is the sample and the average weight calculated is the sample mean now suppose they take repeated random samples from the general population and compute the sample mean for each sample group instead so for north america they pull data for 100 newborn weights recorded in the u s canada and mexico as follows the researcher ends up with a total of 1 200 weights of newborn babies grouped in 12 sets they also collect sample data of 100 birth weights from each of the 12 countries in south america the average weight computed for each 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 sample data the standard deviation and variance measure the variability of the sampling distribution 2types of sampling distributionshere is a brief description of the types of sampling distributions in statistics a population is the entire pool from which a statistical sample is drawn a population may refer to an entire group of people objects events hospital visits or measurements a population can thus be said to be an aggregate observation of subjects grouped together by a common feature 3plotting sampling distributionsa 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 1 200 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 