page_title: Standard error
section_title: Example
hierarchical_section_title: Standard error / Example
caption_attribution_description: English: Photo of a mature Red Drum, aka redfish, channel bass or spottail bass. Caught off the Gulf Coast of Louisiana. This is a mature red drum but not a "bull red," the nickname given to red drum longer than 26 inches.
context_page_description: The standard error is the standard deviation of the sampling distribution of a statistic. The term may also be used for an estimate of that standard deviation taken from a sample of the whole group.
  The average of some part of a group is the usual way to estimate the average for the whole group. It is often too hard or costs too much money to measure the whole group. But if a different sample is measured, it will have an average that is a little bit different from the first sample. The standard error of the mean is a way to know how close the average of the sample is to the average of the whole group. It is a way to know how sure you can be about the average from the sample.
  In real measurements, the true value of the standard deviation of the mean for the whole group is usually not known. So the term standard error is often used to mean a close guess to the true number for the whole group. The more measurements there are in a sample, the closer the guess will be to the true number for the whole group.
context_section_description: For example, there are many redfish in the water of the Gulf of Mexico. To find out how much a 42 cm long redfish weighs on average, it is not possible to measure all of the redfish that are 42 cm long.  Instead, it is possible to measure some of them. The fish that are actually measured are called a sample. The table shows weights for two samples of redfish, all 42 cm long. The average (mean) weight of the first sample is 0.741 kg. The average (mean) weight of the second sample is 0.735 kg, a little bit different from the first sample.  Each of these averages is a little bit different from the average that would come from measuring every 42 cm long redfish (which is not possible anyway).
  The uncertainty in the mean can be used to know how close the average of the samples are to the average that would come from measuring the whole group. The uncertainty in the mean is estimated as the standard deviation for the sample, divided by the square root of the number of samples minus one. The table shows that the uncertainties in the means for the two samples are very close to each other. Also, the relative uncertainty is the uncertainty in the mean divided by the mean, times 100%. The relative uncertainty in this example is 2.38% and 2.50% for the two samples.
  Knowing the uncertainty in the mean, one can know how close the sample average is to the average that would come from measuring the whole group. The average for the whole group is between a) the average for the sample plus the uncertainty in the mean, and b) the average for the sample minus the uncertainty in the mean. In this example, the  average weight for all of the 42 cm long redfish in the Gulf of Mexico is expected to be 0.723–0.759 kg based on the first sample, and 0.717–0.753 based on the second sample.
caption: Example of a redfish (also known as red drum, Sciaenops ocellatus) used in the example.
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