Question

How does standard deviation differ from standard error ?

Answer 1

Standard deviation is a measure of disbursement in statistics. Disbursement tells us how much our data is spread out. Specifically, it talks about how much our data is spread out around the mean or average. Standard error is a mathematical tool used in statistics to measure variability. It enables one to arrive at an estimation of what the standard deviation of a given sample is. It is commonly abbreviated as SE. Let us look at how these two are different from each other.

Complete step-by-step answer:
When we calculate the sample mean we are usually interested not in the mean of this particular sample, but in the mean for individuals of this type—in statistical terms, of the population from which the sample comes.
We usually collect data in order to generalize from them and so use the sample mean as an estimate of the mean for the whole population.
Now the sample mean will vary from sample to sample; the way this variation occurs is described by the sampling distribution of the mean. We can estimate how much sample means will vary from the standard deviation of this sampling distribution, which we call the standard error (SE) of the estimate of the mean.
As the standard error is a type of standard deviation, confusion is understandable. Another way of considering the standard error is as a measure of the precision of the sample mean.
The standard error of the sample mean depends on both the standard deviation and the sample size, by the simple relation $SE=\dfrac{SD}{\sqrt{Sample\text{ size}\text{.}}}$ , where SD is Standard Deviation.
The formula for calculating Standard Deviation is as follows :
$\Rightarrow SD=\sqrt{\dfrac{\sum{{{\left| x-\overline{x} \right|}^{2}}}}{n}}$ , where $x$ represents each value from the population,$\overline{x}$ represents the population mean,$n$ represents the size of the population.
The formula for calculating Standard Error is as follows :
$\Rightarrow SE=\dfrac{SD}{\sqrt{n}}$ , where $n$ represents the size of the population.

Note: Sometimes Standard Deviation is represented by sigma$\left( \sigma \right)$. It is very important to know the definition and the difference between Standard Deviation and Standard Error. We should also know the relation between them. We should have enough practice since the calculations in statistics are quite lengthy and time taking. We should be careful while solving too since there is a lot of scope for calculation errors.