A:

The standard deviation, or SD, measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean, or SEM, measures how far the sample mean of the data is likely to be from the true population mean. The SEM is always smaller than the SD.

The formula for the SEM is the standard deviation divided by the square root of the sample size. The formula for the SD requires a few steps.

1. First, take the square of the difference between each data point and the sample mean, finding the sum of those values.
2. Then, divide that sum by the sample size minus one, which is the variance.
3. Finally, take the square root of the variance to get the SD.

The SEM describes how precise the mean of the sample is versus the true mean of the population. As the size of the sample data grows larger, the SEM decreases versus the SD. As the sample size increases, the true mean of the population is known with greater specificity. In contrast, increasing the sample size also provides a more specific measure of the SD. However, the SD may be more or less depending on the dispersion of the additional data added to the sample.

The SD is a measure of volatility and can be used as a risk measure for an investment. Assets with higher prices have a higher SD than assets with lower prices. The SD can be used to measure the importance of a price move in an asset. Assuming a normal distribution, around 68% of daily price changes are within one SD of the mean, with around 95% of daily price changes within two SDs of the mean.

RELATED FAQS
1. ### How do I calculate the standard error using Matlab?

Learn how to calculate the standard error for a sample statistical measure, such as the sample mean, using standard Matlab ... Read Answer >>
2. ### When is it better to use systematic over simple random sampling?

Learn when systematic sampling is better than simple random sampling, such as in the absence of data patterns and when there ... Read Answer >>
3. ### What are the advantages of using a simple random sample to study a larger population?

Learn how simple random sampling works and what advantages it offers over other sampling methods when selecting a research ... Read Answer >>
4. ### What is the difference between standard deviation and z score?

Understand the basics of standard deviation and Z-score; learn how each is calculated and used in the assessment of market ... Read Answer >>
5. ### What assumptions are made when conducting a t-test?

Learn what a t-test is and discover the five standard assumptions made regarding the validity of sampling and data used in ... Read Answer >>
6. ### What is the best measure of a stock's volatility?

Understand what metrics are most commonly used to assess a security's volatility compared to its own price history and that ... Read Answer >>
Related Articles
1. Investing

### How to Use Stratified Random Sampling

Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroup’s ...

### Trading with Gaussian models of statistics

The study of statistics originated from Carl Friedrich Gauss and helps us understand markets, prices and probabilities, among other applications.

### Using Bollinger Bands to Gauge Trends

Learn three Bollinger Bands® strategies that can be used for analysis or generating trade signals.

This intraday strategy picks tops and bottoms based on a clear recovery following an extreme move.
5. Investing

### Redefining Investor Risk

Changing the way you think about time and risk can change the way you invest.
6. Investing

### Is It Time to Give Up on SandRidge Energy? (SD)

When oil was over \$90 a barrel, there was a lot to like about SandRidge Energy (NYSE: SD). The company had a prime position in an emerging oil play and so it levered up in an effort to fuel ...

### How To Convert Value At Risk To Different Time Periods

Volatility is not the only way to measure risk. Learn about the "new science of risk management".
8. Investing

### Optimize your portfolio using normal distribution

Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
9. Investing

### Understanding Volatility Measurements

How do you choose a fund with an optimal risk-reward combination? Here we teach you about standard deviation, beta and more.
RELATED TERMS
1. ### Standard Error

Standard error is the standard deviation of a sample population.
2. ### Sampling

Sampling is a process used in statistical analysis in which a ...
3. ### Sample Size Neglect

Sample size neglect occurs when an individual infers too much ...
4. ### Volatility

Volatility measures how much the price of a security, derivative, ...
5. ### Stratified Random Sampling

Stratified random sampling is a method of sampling that involves ...
6. ### Non-Sampling Error

A non-sampling error is an error that results during data collection, ...
Hot Definitions
1. ### Diversification

Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
2. ### Intrinsic Value

Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
3. ### Current Assets

Current assets is a balance sheet item that represents the value of all assets that can reasonably expected to be converted ...
4. ### Volatility

Volatility measures how much the price of a security, derivative, or index fluctuates.
5. ### Money Market

The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
6. ### Cost of Debt

Cost of debt is the effective rate that a company pays on its current debt as part of its capital structure.