# Standard Deviation vs. Standard Error: What's the Difference?

Edited by Aimie Carlson || By Janet White || Published on November 14, 2023
"Standard Deviation" measures the spread of individual data points around the mean, while "Standard Error" gauges the accuracy of a sample mean estimate relative to the population mean.

## Key Differences

"Standard Deviation" quantifies the dispersion or spread of data points in a dataset from the mean value. On the other hand, "Standard Error" gives an estimate of how much a sample mean deviates from the population mean.
When observing "Standard Deviation," one assesses the variability present within a single dataset. In contrast, the "Standard Error" is especially useful in hypothesis testing or determining confidence intervals, focusing on the precision of the sample mean.
An essential distinction lies in the application. "Standard Deviation" is widely used across datasets to measure variability. Meanwhile, "Standard Error" plays a critical role when researchers are interested in the reliability of their sample mean as an estimate of the population mean.
Though both terms are rooted in statistical variance and revolve around means, their core significance diverges. "Standard Deviation" provides a sense of the dataset's distribution, while "Standard Error" evaluates the sampling variability when estimating a population parameter.

## Comparison Chart

### Definition

Dispersion of individual data points.
Precision of the sample mean as an estimator.

### Application

Used to quantify spread in single datasets.
Used in hypothesis testing & determining confidence intervals.

### Relation to Variability

Measures variability within a dataset.
Measures variability of the sample mean estimate.

### Depends on

Data points in the dataset.
Sample size and standard deviation.

### Calculation

Square root of the variance.
Standard Deviation divided by the square root of sample size.

## Standard Deviation and Standard Error Definitions

#### Standard Deviation

A measure of data dispersion from the mean.
A low Standard Deviation indicates that the data points are close to the mean.

#### Standard Error

A measure of the variability of the sample mean.
Standard Error helps in determining the width of confidence intervals for population parameters.

#### Standard Deviation

Quantification of the amount data varies around the average.
High Standard Deviation suggests data points are spread over a wide range.

#### Standard Error

Quantifies how much sample means vary around the population mean.
Polls often report a margin of error based on the Standard Error.

#### Standard Deviation

A statistical tool to gauge dataset variability.
Based on the Standard Deviation, financial analysts make investment decisions.

#### Standard Error

Reflects the precision of a sample mean as a population mean estimate.
Researchers might increase the sample size to reduce the Standard Error.

#### Standard Deviation

The average distance of each data point from the mean.
Standard Deviation helps in assessing the consistency in production processes.

#### Standard Error

The standard deviation of sampling distribution of the sample mean.
Standard Error decreases as sample size increases, given a fixed population size and standard deviation.

#### Standard Deviation

Represents the spread of data in relation to its average.
In IQ tests, a Standard Deviation of 15 is commonly used.

#### Standard Error

An estimation of the sample mean's deviation from the population mean.
A smaller Standard Error suggests the sample mean is a reliable estimator of the population mean.

## FAQs

#### Does a high "Standard Deviation" mean greater variability?

Yes, a high "Standard Deviation" indicates that data points are spread out over a wider range from the mean.

#### How is "Standard Error" computed?

"Standard Error" is computed by dividing the "Standard Deviation" by the square root of the sample size.

#### Can "Standard Error" be used for parameters other than the mean?

Yes, "Standard Error" can refer to the standard deviation of other sample estimators, not just the mean.

#### Is "Standard Deviation" affected by outliers?

Absolutely, "Standard Deviation" is sensitive to outliers, which can inflate its value.

#### Is "Standard Error" inversely related to sample size?

Yes, "Standard Error" typically decreases as the sample size increases, assuming a fixed standard deviation.

#### Does "Standard Deviation" offer insights into data distribution shape?

While "Standard Deviation" indicates spread, it doesn't specify the exact shape of the data distribution; other measures like skewness are needed.

#### What happens to "Standard Deviation" if all data values are identical?

If all data values are the same, the "Standard Deviation" will be zero, indicating no variability.

#### How is "Standard Error" useful in research?

"Standard Error" gauges the accuracy of the sample mean as an estimate of the population mean, aiding in hypothesis testing.

#### What does a decreasing "Standard Error" signify in sequential sampling?

A decreasing "Standard Error" suggests increasing precision in estimating the population parameter.

#### What does "Standard Deviation" represent in statistics?

"Standard Deviation" represents the amount of variation or dispersion from the average in a dataset.

#### Can "Standard Deviation" be negative?

No, "Standard Deviation" is always non-negative since it represents a distance or spread.

#### Is "Standard Error" specific to a sample or a population?

"Standard Error" typically refers to samples, gauging the precision of a sample estimator relative to the population parameter.

#### How does "Standard Deviation" relate to variance?

"Standard Deviation" is the square root of variance, another measure of data dispersion.

#### How does "Standard Error" relate to confidence intervals?

"Standard Error" helps determine the width of confidence intervals, with smaller errors leading to narrower intervals.

#### Can transformations change a dataset's "Standard Deviation"?

Yes, certain transformations can alter the "Standard Deviation" of a dataset.

#### Why might researchers prefer to report "Standard Error" over "Standard Deviation"?

Researchers might report "Standard Error" to emphasize the reliability of the sample mean as an estimate for the population mean.

#### Is "Standard Deviation" used in the bell curve or normal distribution?

Yes, in a normal distribution, about 68% of data lies within one "Standard Deviation" from the mean.

#### Can two datasets have the same "Standard Deviation" but different means?

Yes, two datasets can share the same "Standard Deviation" but differ in their average values.

#### How does sample size affect "Standard Error" in relation to "Standard Deviation"?

While "Standard Deviation" remains unchanged, increasing sample size generally reduces "Standard Error."

#### Is "Standard Error" larger or smaller than "Standard Deviation"?

Typically, "Standard Error" is smaller than "Standard Deviation" since it's derived by dividing the latter by the square root of the sample size.