I feel like people might be overcomplicating this. If you take a sample from a population, you get two main statistics from it: The mean, and the deviation. One describes the center of the data, the other the distribution around it. Imagine you kept drawing new samples again and again. You can make a list of the means, right? They should all be fairly close, but the random sampling means they're all slightly different. That list of means has it's own mean - and it's own deviation. That deviation is the standard error of the mean. It's a measure of the distribution of means in many samples of the same population. Now, the formula you're probably familiar with obviously doesn't draw many samples from the population! It's an estimate of the SEM, not the actual SEM. It uses a single sample deviation and the number of elements in that sample to make the estimate. Answer from automated_reckoning on reddit.com
Investopedia
investopedia.com › ask › answers › 042415 › what-difference-between-standard-error-means-and-standard-deviation.asp
Standard Error of the Mean vs. Standard Deviation
March 24, 2025 - You're told both pay an average of $5,000 a month, but there's a catch: Job A has a traditional salary that pays $5,000 every month according to a contract. Job B is gig work, where you might earn $7,500 one month and $2,000 the next. They have the same average but mean something very different when you are planning your rent or mortgage payments. Situations like this are why statistical measures like standard deviation (often symbolized as σ) and standard error of the mean (SEM) are employed—they give you more depth than simple averages.
Biostatisticsbydesign
biostatisticsbydesign.com › blog › 2019 › 1 › 5 › when-to-report-the-standard-deviation-vs-the-standard-error
When to Report the Standard Deviation vs. the Standard Error — Biostatistics By Design
January 5, 2019 - Thus, when you compare the means and declare a difference between those means (reject the null hypothesis), you want to include a measure of how much confidence you have that they are truly different. Therefore, in this case, I would report the standard errors. Still having trouble wrapping your brain around the difference between the standard deviation and the standard error?
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Reddit
reddit.com › r/statistics › eli5: difference between standard deviation and standard error
r/statistics on Reddit: ELI5: Difference between standard deviation and standard error
May 29, 2017 -
Could someone explain this with possibly an example? Thanks!
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Standard deviation is a characteristic of a random variable describing how dispersed samples from it are, standard error (of mean) is a description of how confident you are in where the variable's mean lies. The more samples you have the smaller your standard error because you can be more confident of where the mean lies, but the underlying deviation is the same. If the standard deviation is larger, then your confidence in where the mean lies will also be broadened and you will need more samples to get to the same standard error.
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If you take some sample statistic like a mean (or a standard deviation or a minimum or a median or an interquartile range or a regression slope) and you compare them across a number of samples, they vary from sample to sample. That is, things like sample means have their own distribution (sometimes called a sampling distribution). That distribution has its own standard deviation, and we can approximately work out that standard deviation by performing a calculation on the standard deviation of the original numbers from a single sample. So when we want the standard deviation of the distribution of some statistic like a sample mean we can work out an estimate of it from the sample we have. We call that estimate the standard error of the statistic. So for example we can get the standard deviation of the distribution of a sample mean (which is called the standard error of the mean) by taking the standard deviation of the sample we calculated the mean from and dividing by √n . (As you average more values, the sample mean becomes less variable -- it varies less from the population mean) For many other statistics the standard error calculation also requires some assumption about the shape of the distribution but for sample means it doesn't. So for example, consider this little sample of counts: 5 10 13 11 7 6 6 11 12 it has mean 9 and standard deviation 3. The estimated standard deviation of the distribution of the sample mean itself is 3/√9 = 1. That is, the standard error of the mean is 1.
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC3487226
What to use to express the variability of data: Standard deviation or standard error of mean? - PMC
SEM quantifies uncertainty in estimate of the mean whereas SD indicates dispersion of the data from mean. As readers are generally interested in knowing the variability within sample, descriptive data should be precisely summarized with SD. Use of SEM should be limited to compute CI which measures ...
6 Sigma
6sigma.us › articles › understanding the difference: standard error vs. standard deviation
Standard Error vs Standard Deviation: Finding the Difference - SixSigma.us
April 22, 2025 - While SD measures variability within a dataset, SE estimates the precision of a sample statistic. This distinction becomes particularly important when deciding which measure to use in your analysis and reporting.
CareerFoundry
careerfoundry.com › en › blog › data-analytics › standard-error-vs-standard-deviation
Standard Error vs Standard Deviation: What's the Difference?
May 11, 2023 - As part of your analysis, it’s important to understand how accurately or closely the sample data represents the whole population. In other words, how applicable are your findings? This is where statistics like standard deviation and standard error come in. In this post, we’ll explain exactly what standard deviation and standard error mean, as well as the key differences between them.
Wikipedia
en.wikipedia.org › wiki › Standard_error
Standard error - Wikipedia
October 10, 2025 - This often leads to confusion about their interchangeability. However, the mean and standard deviation are descriptive statistics, whereas the standard error of the mean is descriptive of the random sampling process.
University of Southampton Library
library.soton.ac.uk › variance-standard-deviation-and-standard-error
Maths and Stats - Variance, Standard Deviation and Standard Error - LibGuides@Southampton at University of Southampton Library
Standard deviation is used to describe the data, and standard error is used to describe statistical accuracy. It is easier to calculate these using software than by hand. Variance is a measure of how far the observed values in a dataset fall from the arithmetic mean, and is therefore a measure ...
Reddit
reddit.com › r/statistics › what is the difference between standard deviation and standard error of the mean?
r/statistics on Reddit: What is the difference between standard deviation and standard error of the mean?
February 4, 2019 -
Would any kind soul provide me with an example to try understand it?
Top answer 1 of 8
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I feel like people might be overcomplicating this. If you take a sample from a population, you get two main statistics from it: The mean, and the deviation. One describes the center of the data, the other the distribution around it. Imagine you kept drawing new samples again and again. You can make a list of the means, right? They should all be fairly close, but the random sampling means they're all slightly different. That list of means has it's own mean - and it's own deviation. That deviation is the standard error of the mean. It's a measure of the distribution of means in many samples of the same population. Now, the formula you're probably familiar with obviously doesn't draw many samples from the population! It's an estimate of the SEM, not the actual SEM. It uses a single sample deviation and the number of elements in that sample to make the estimate.
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Imagine you roll an ordinary six-sided die (a fair one) The population mean outcome is 3.5 and the population standard deviation is about 1.7 If you roll it a whole bunch of times the sample mean and and sample standard deviation of the collection of rolls will be very close to 3.5 and 1.7 Now do something different. Instead of keeping a record of each roll, you're going to roll the die 4 times, take the average of those 4 rolls and record that. e.g. if you roll 6, 5, 6, 1 the average is 4.5 What's the population standard deviation of this collection of averages? Since we're averaging samples of size 4, it turns out to be half as big as the population standard deviation of individual rolls (we can prove this but I don't expect the proof is something you're interested in). If you repeat that experiment a whole bunch of times, the sample standard deviation of those averages comes out very close to that population value (1.7/2 = 0.85) We have a special name for the population standard deviation of the distribution of averages -- it's "the standard error of the mean". (More typically, we don't know the population value and have to estimate it from a sample.)
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC4452664
Standard deviation and standard error of the mean - PMC
However, the mean alone is not sufficient when attempting to explain the shape of the distribution; therefore, many medical literatures employ the standard deviation (SD) and the standard error of the mean (SEM) along with the mean to report statistical analysis results [2]. The objective of this article is to state the differences with regard to the use of the SD and SEM, which are used in descriptive and statistical analysis of normally distributed data, and to propose a standard against which statistical analysis results in medial literatures can be evaluated.
Statistics By Jim
statisticsbyjim.com › home › blog › difference between standard deviation and standard error
Difference Between Standard Deviation and Standard Error - Statistics By Jim
June 24, 2025 - High values of either statistic indicate more dispersion. However, that’s where the similarities end. The standard deviation is not the same as the standard error. ... Standard deviation: Quantifies the variability of values in a dataset. It assesses how far a data point likely falls from the mean.
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To complete the answer to the question, Ocram nicely addressed standard error but did not contrast it to standard deviation and did not mention the dependence on sample size. As a special case for the estimator consider the sample mean. The standard error for the mean is $\sigma \, / \, \sqrt{n}$ where $\sigma$ is the population standard deviation. So in this example we see explicitly how the standard error decreases with increasing sample size. The standard deviation is most often used to refer to the individual observations. So standard deviation describes the variability of the individual observations while standard error shows the variability of the estimator. Good estimators are consistent which means that they converge to the true parameter value. When their standard error decreases to 0 as the sample size increases the estimators are consistent which in most cases happens because the standard error goes to 0 as we see explicitly with the sample mean.
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Here is a more practical (and not mathematical) answer:
- The SD (standard deviation) quantifies scatter — how much the values vary from one another.
- The SEM (standard error of the mean) quantifies how precisely you know the true mean of the population. It takes into account both the value of the SD and the sample size.
- Both SD and SEM are in the same units -- the units of the data.
- The SEM, by definition, is always smaller than the SD.
- The SEM gets smaller as your samples get larger. This makes sense, because the mean of a large sample is likely to be closer to the true population mean than is the mean of a small sample. With a huge sample, you'll know the value of the mean with a lot of precision even if the data are very scattered.
- The SD does not change predictably as you acquire more data. The SD you compute from a sample is the best possible estimate of the SD of the overall population. As you collect more data, you'll assess the SD of the population with more precision. But you can't predict whether the SD from a larger sample will be bigger or smaller than the SD from a small sample. (This is a simplification, not quite true. See comments below.)
Note that standard errors can be computed for almost any parameter you compute from data, not just the mean. The phrase "the standard error" is a bit ambiguous. The points above refer only to the standard error of the mean.
(From the GraphPad Statistics Guide that I wrote.)
Scribbr
scribbr.com › home › what is standard error? | how to calculate (guide with examples)
What Is Standard Error? | How to Calculate (Guide with Examples)
June 22, 2023 - You can decrease standard error by increasing sample size. Using a large, random sample is the best way to minimize sampling bias. ... The standard deviation describes variability within a single sample.
YouTube
youtube.com › statquest with josh starmer
Standard Deviation vs Standard Error, Clearly Explained!!!
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Published March 20, 2017 Views 148K
Greenbook
greenbook.org › insights › research-methodologies › how-to-interpret-standard-deviation-and-standard-error-in-survey-research
How to Interpret Standard Deviation and Standard Error in Survey Research — Greenbook
Most tabulation programs, spreadsheets or other data management tools will calculate the SD for you. More important is to understand what the statistics convey. The Standard Error ("Std Err" or "SE"), is an indication of the reliability of the mean.
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC7746895
Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which - PMC
Many authors are unsure of whether to present the mean along with the standard deviation (SD) or along with the standard error of the mean (SEM). The SD is a descriptive statistic that estimates the scatter of values around the sample mean; hence, the SD describes the sample.
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC3148365
In Brief: Standard Deviation and Standard Error - PMC
For instance, when reporting the survival probability of a sample we should provide the standard error together with this estimated probability. However, because the confidence interval is more useful and readable than the standard error, it can be provided instead as it avoids having the readers do the math. If a researcher is interested in estimating the mean tumor size in the population, then he or she would have to provide the mean and standard deviation of tumor size to describe the sample observed and the standard error or confidence interval to infer to the population.
Quora
quora.com › When-do-you-use-standard-error-of-the-mean-rather-than-the-standard-deviation
When do you use standard error of the mean rather than the standard deviation? - Quora
Answer (1 of 3): Standard error represents the standard deviation of an estimator. It should be used when you are making inferences or trying to describe your estimate. The standard deviation is a parameter of the population (not the sample).
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC1255808
Standard deviations and standard errors - PMC
So, if we want to say how widely scattered some measurements are, we use the standard deviation. If we want to indicate the uncertainty around the estimate of the mean measurement, we quote the standard error of the mean. The standard error is most useful as a means of calculating a confidence ...
DataScience+
datascienceplus.com › standard-deviation-vs-standard-error
Standard deviation vs Standard error | DataScience+
Note that the standard error of the mean depends on the sample size, the standard error of the mean shrink to 0 as sample size increases to infinity. It depends. If the message you want to carry is about the spread and variability of the data, then standard deviation is the metric to use.