Statistics By Jim
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Standard Error of the Mean (SEM) - Statistics By Jim
June 24, 2025 - In this post the standard error of the mean is calculated from a single sample by using the formula (standard deviation obtained from a single sample divided by square root of the sample size).
statistical property
Wikipedia
en.wikipedia.org › wiki › Standard_error
Standard error - Wikipedia
October 10, 2025 - This is because as the sample size ... and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size....
Understanding Standard error calculation
we might as well call this population standard deviation because it represents all the samples. We call it the population standard deviation because it is. The assumption here is that we're working with a random sample from some distribution with standard deviation σ. If that's true, then the sample mean has standard deviation σ/√n. You can definitely draw multiple samples if you want to visualize the standard error (e.g. as part of a simulation), but it's very important to develop the understanding that a single sample mean is a random variable, and that the standard error it its standard deviation. Standard deviation from the samples which is equal to the population standard deviation is called the unbiased estimate of population standard deviation. The sample standard deviation is not an unbiased estimate of the population standard deviation. Indeed, it's generally very difficult to derive unbiased estimators of the standard deviation (e.g. there is no unbiased estimator for a normal SD in terms of elementary functions). More on reddit.com
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May 10, 2024[Q] Explain to me how Standard Error is able to do what it does?
In very, very general terms, the central limit theorem says that—under certain constraints—if you take a lot of samples from the same population, the means of all those samples will form a normal distribution no matter what the distribution of the population is. Furthermore, the mean of that sampling distribution will be the mean of the population. The standard error is basically the standard deviation of that derived normal distribution. In other words, about 68% of all the sample means will be within one standard error of the mean of that sampling distribution. So with the standard error you can make some inferences about how the mean of your sample relates to the mean of the population based on the sample size (or rather, the square root of it). More on reddit.com
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October 15, 2021[Question] How do you calculate the standard error?
How do you calculate the standard error? A standard error is the standard deviation of the sampling distribution of some statistic. When the statistic is a sample mean of independent identically distributed values, its standard error is σ/√n where σ2 is the variance of the original population of values. This is specifically the standard error of the mean. When σ is unknown it is typically estimated by s, so s/√n is an estimated standard error of the mean. So What statistic are you asking about the standard error of? If it is the sample mean you want a standard error of, we can't tell what you might be doing wrong from this. You'd need to show some examples of the information that was given (verbatim, including any description) and cases where you had the right or the wrong answer. With the standard error of the mean, normality doesn't really come into it. It follows from basic properties of variances. I am confused which one to use and when. I am unclear what you mean by "which one". Are you saying you can't tell when a question is asking for a variance or a standard deviation or a standard error of the mean? More on reddit.com
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March 29, 2024What is the difference between standard deviation and standard error of the mean?
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. More on reddit.com
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February 4, 2019What is standard error?
The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.
scribbr.com
scribbr.com › home › what is standard error? | how to calculate (guide with examples)
What Is Standard Error? | How to Calculate (Guide with Examples)
What’s the difference between standard error and standard deviation?
Standard error and standard deviation are both measures of variability. The standard deviation reflects variability within a sample, while the standard error estimates the variability across samples of a population.
scribbr.com
scribbr.com › home › what is standard error? | how to calculate (guide with examples)
What Is Standard Error? | How to Calculate (Guide with Examples)
What’s the difference between a point estimate and an interval estimate?
Using descriptive and inferential statistics, you can make two types of estimates about the population: point estimates and interval estimates. · A point estimate is a single value estimate of a parameter. For instance, a sample mean is a point estimate of a population mean. · An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate. · Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.
scribbr.com
scribbr.com › home › what is standard error? | how to calculate (guide with examples)
What Is Standard Error? | How to Calculate (Guide with Examples)
Videos
BYJUS
byjus.com › maths › standard-error-of-the-mean
How to calculate standard error of mean?
December 9, 2021 - SEM represents an estimate of standard deviation, which has been calculated from the sample. The formula for standard error of the mean is equal to the ratio of the standard deviation to the root of sample size.
Indeed
indeed.com › career guide › career development › what is the standard error of the mean (sem)?
What Is the Standard Error of the Mean (SEM)? | Indeed.com
October 15, 2023 - The following table outlines the differences between the two: Related: Descriptive vs. Inferential Statistics: Differences and Ways to Measure · The formula for the standard error of the mean is expressed as:SE = σ/√n
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 - Example: Using the standard error formulaTo estimate the standard error for math SAT scores, you follow two steps. First, find the square root of your sample size (n). Next, divide the sample standard deviation by the number you found in step one.
Standard Deviation Calculator
standarddeviationcalculator.io › standard-error-calculator
Standard Error Calculator
It is simply calculated using the standard error formula or dividing the sample standard deviation of given data with the root of sample size. Follow the below steps to find SE-value: First, note the data in which form is given. If data is in the form of summary form then simply put values ...
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
November 10, 2025 - The main difference between the standard deviation and the standard error is that the standard deviation is a type of descriptive statistics, used to summarise the data, whereas the standard error of the mean describes the random sampling process, and is an estimation rather than a definite value like the standard deviation is.
AnalystPrep
analystprep.com › home › standard error of the sample mean
Standard Error of the Mean | CFA Level 1 - AnalystPrep
The standard error (SE) of the sample mean refers to the standard deviation of the distribution of the sample means. It gives analysts an estimate of the variability they would expect if they were to draw multiple samples from the same population. While the standard deviation measures the variability obtained within one sample, the standard error gives an estimate of the variability among many samples. Provided the population standard deviation, σ, is known, analysts use the following formula to estimate the standard error of the sample mean, denoted as σx:
Published February 11, 2025
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 - Most succinctly put, standard deviation is about where the data are clustered in one sample data, while SEM is where the means would be clustered around many samples taken of a given set of things. We tackle both below. Standard deviation describes how much variability—or fluctuation—exists within a data set. The standard error of the mean (SEM) indicates how accurately a data set represents the true population by comparing the dataset's average to the population's average.
Ablebits
ablebits.com › ablebits blog › excel › calculations › how to calculate standard error of mean in excel
How to calculate standard error of mean in Excel
May 18, 2023 - Get the sample size, i.e. the total number of values, with the help of the COUNT function. Determine the square root of the sample size using the SQRT function. Divide the standard deviation by the square root of the sample size. The generic ...
Uib
biostats.w.uib.no › 5-calculate-the-standard-error-of-the-mean-sem-2
5. Calculate the standard error of the mean (SEM) – bioST@TS
The standard error of the mean may be calculated by dividing the standard deviation by the square root of the number of values in the dataset. There is no direct function in MS Excel to get it automatically.
AllMath
allmath.com › standard-error-calculator.php
Standard Error Calculator
Standard Error (SE) = (Standard Deviation of the Sample) / √Sample Size ... It is calculated, by dividing the standard deviation of the data set by the square root of the sample size of data.
Statistics LibreTexts
stats.libretexts.org › bookshelves › applied statistics › biological statistics (mcdonald) › 3: descriptive statistics
3.3: Standard Error of the Mean - Statistics LibreTexts
January 8, 2024 - Fortunately, you can estimate the ... The standard error of the mean is estimated by the standard deviation of the observations divided by the square root of the sample size....
Reddit
reddit.com › r/askstatistics › understanding standard error calculation
r/AskStatistics on Reddit: Understanding Standard error calculation
May 10, 2024 -
Hello!! I am trying to understand the workings behind the formula for standard error but I am getting very confused.
So from my understanding, standard error is the standard deviation of sample means, and the formula for it is:
n = sample size Standard error = standard deviation/sqrt(n)
I am confused as to whose standard deviation is this?
But this is what I gathered online; since the standard deviation for all the different samples is different, we need a standard deviation that is representative of all the samples, we might as well call this population standard deviation because it represents all the samples. Standard deviation from the samples which is equal to the population standard deviation is called the unbiased estimate of population standard deviation. So we are looking at calculating the unbiased estimate of population standard deviation from the sample dataset. Which means we have to consider n - 1 for the denominator, because of freedom of degrees.
Okay, now we have the unbiased estimate of population standard deviation, which is representative of all the standard deviations of the different samples.
Hence, standard error = unbiased estimate of population standard deviation//sqrt(n)
Is this correct? Any help is appreciated, thank you!!!!!!!!
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we might as well call this population standard deviation because it represents all the samples. We call it the population standard deviation because it is. The assumption here is that we're working with a random sample from some distribution with standard deviation σ. If that's true, then the sample mean has standard deviation σ/√n. You can definitely draw multiple samples if you want to visualize the standard error (e.g. as part of a simulation), but it's very important to develop the understanding that a single sample mean is a random variable, and that the standard error it its standard deviation. Standard deviation from the samples which is equal to the population standard deviation is called the unbiased estimate of population standard deviation. The sample standard deviation is not an unbiased estimate of the population standard deviation. Indeed, it's generally very difficult to derive unbiased estimators of the standard deviation (e.g. there is no unbiased estimator for a normal SD in terms of elementary functions).
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The standard error of the (sample) mean is the standard deviation of the distribution of all possible sample means. It is numerically equal to the population SD divided by the square root of the sample size
Reddit
reddit.com › r/statistics › [q] explain to me how standard error is able to do what it does?
r/statistics on Reddit: [Q] Explain to me how Standard Error is able to do what it does?
October 15, 2021 -
My understanding is that standard error is essentially a measure of how different the means you obtain when you sample from a population will be. According to statistical theory, if you have a population, and you take a sample of this population, you can calculate standard deviation by comparing each value to the mean of your sample. But then, when you take that number and simply divide it by the square root of your sample size, then voila, you magically know how spread out the mean of every single sample you could ever take of that population is.
To me, that seems like a HUGE stretch that you can make such a huge assumption. It is already a bit of a stretch to think that your sample is a decent representation of an actual population mean, and sure, I get that these formulas are actually just estimates rather than concrete math. But I never would have guessed that the deviation of a sample, divided by a modification of the sample size, could tell you how much any mean sample could ever vary, ever.
Am I way off in assuming this? Am I missing something that should make me think more clearly about this all?
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In very, very general terms, the central limit theorem says that—under certain constraints—if you take a lot of samples from the same population, the means of all those samples will form a normal distribution no matter what the distribution of the population is. Furthermore, the mean of that sampling distribution will be the mean of the population. The standard error is basically the standard deviation of that derived normal distribution. In other words, about 68% of all the sample means will be within one standard error of the mean of that sampling distribution. So with the standard error you can make some inferences about how the mean of your sample relates to the mean of the population based on the sample size (or rather, the square root of it).
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Standard error is just the standard deviation of the sample mean (or whatever estimator you are interested in). The formula is not an estimate - it's an exact solution that you get by deriving the sample variance of the sample mean, then taking the square root. Technically it's a biased estimator, but that's a separate thing. I think you're overstating what the standard error tells you - it's a confidence interval. It tells you nothing about how good THAT specific standard error is. Rather, it tells you that about 68 percent of standard error intervals contain the population value for the quantity of interest.
Outlier
articles.outlier.org › what-is-standard-error-in-statistics
What Is Standard Error? Statistics Calculation and Overview | Outlier
April 13, 2023 - SEMSEM and is equal to the population standard deviation (σ) divided by the square root of the sample size ( ... If the population standard deviation is unknown, you can estimate the standard error by using the sample standard deviation ( ... ...
Reddit
reddit.com › r/statistics › [question] how do you calculate the standard error?
r/statistics on Reddit: [Question] How do you calculate the standard error?
March 29, 2024 -
Guys up until this point I thought standard error was s/sqrt(n) where s is the standard deviation approximation and n is the number of samples. This is usually correct when I solve problems related to normal distriubtion confidence interval. In other cases, this doesn't work and I need to use the square root of the variance which doesn't give the same answer as before. I am confused which one to use and when.
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How do you calculate the standard error? A standard error is the standard deviation of the sampling distribution of some statistic. When the statistic is a sample mean of independent identically distributed values, its standard error is σ/√n where σ2 is the variance of the original population of values. This is specifically the standard error of the mean. When σ is unknown it is typically estimated by s, so s/√n is an estimated standard error of the mean. So What statistic are you asking about the standard error of? If it is the sample mean you want a standard error of, we can't tell what you might be doing wrong from this. You'd need to show some examples of the information that was given (verbatim, including any description) and cases where you had the right or the wrong answer. With the standard error of the mean, normality doesn't really come into it. It follows from basic properties of variances. I am confused which one to use and when. I am unclear what you mean by "which one". Are you saying you can't tell when a question is asking for a variance or a standard deviation or a standard error of the mean?
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This guide covers all the basics and provides easy-to-follow examples. It might be useful to you https://www.futuresavvy.co.uk/tips-tricks/how-to-calculate-standard-error-in-excel
Influential Points
influentialpoints.com › Training › standard_error_of_the_mean-principles-properties-assumptions.htm
Standard error of the mean- Principles
The standard error of the mean is the standard deviation of the sampling distribution of the mean. In other words it is the standard deviation of a large number of sample means of the same sample size drawn from the same population. The term standard error of the mean is commonly (though ...
R-bloggers
r-bloggers.com › r bloggers › how to calculate the standard error of the mean in r
How to Calculate the Standard Error of the Mean in R | R-bloggers
December 7, 2021 - In another way, the standard error of the mean is a metric for determining how widely values in a dataset are spread out. The ratio of the standard deviation to the root of the sample size is the formula for the standard error of the mean.
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 - Purpose: To estimate how much sample means would vary if we repeated the sampling process many times. Formula: SE = SD / √n, where SD is the standard deviation of the sample and n is the sample size.