Why standard deviation

The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population. However, as we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation. These two standard deviations - sample and population standard deviations - are calculated differently.

In statistics, we are usually presented with having to calculate sample standard deviations, and so this is what this article will focus on, although the formula for a population standard deviation will also be shown.

We are normally interested in knowing the population standard deviation because our population contains all the values we are interested in. Therefore, you would normally calculate the population standard deviation if: 1 you have the entire population or 2 you have a sample of a larger population, but you are only interested in this sample and do not wish to generalize your findings to the population.

However, in statistics, we are usually presented with a sample from which we wish to estimate generalize to a population, and the standard deviation is no exception to this. Therefore, if all you have is a sample, but you wish to make a statement about the population standard deviation from which the sample is drawn, you need to use the sample standard deviation.

To change or withdraw your consent choices for Investopedia. At any time, you can update your settings through the "EU Privacy" link at the bottom of any page. These choices will be signaled globally to our partners and will not affect browsing data. We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Your Money. Personal Finance.

Your Practice. Popular Courses. Financial Ratios Guide to Financial Ratios. Table of Contents Expand. What Is Standard Deviation? Understanding the Standard Deviation.

Key Takeaways: Standard deviation measures the dispersion of a dataset relative to its mean. A volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low. Article Sources. Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts.

We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy. Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation.

This compensation may impact how and where listings appear. Osama Elbahr Thanks for your illustrations. But, can you clarify when to incorporate SE in our research results and how to interpret? Thanks again 19th February at pm Reply to Osama. Guru I was not able to understand standard error. Rohit Standard Deviation is the square root of variance, so its kind of trivial to state the conclusion about the increasing standard error with respect to standard error.

It is a good write up 6th October at pm Reply to Rohit. Emma Carter Thank you for flagging the symbol errors on the page Rohit.

Wesley Hi, Thank you! Emma Carter Hi Wesley. Kennedy Nashiana This is well simplified. Musa sale How do i differentiate variance,standard deviation and standard error 14th March at pm Reply to Musa. DG Shankar Very Good.

Subscribe to our newsletter You will receive our monthly newsletter and free access to Trip Premium. In general, the larger the standard deviation of a data set, the more spread out the individual points are in that set. The technical definition of standard deviation is somewhat complicated. First, for each data value, find out how far the value is from the mean by taking the difference of the value and the mean.

Then, square all of those differences. Then, take the average of those squared differences. Finally, take the square root of that average. The reason we go through such a complicated process to define standard deviation is that this measure appears as a parameter in a number of statistical and probabilistic formulas, most notably the normal distribution. Wikimedia Commons The normal distribution is an extremely important tool in statistics.

The shape of a normal distribution is a bell-shaped curve, like the one in the image. That curve shows, roughly speaking, how likely it is that a random process following a normal distribution will take on a particular value along the horizontal axis. Values near the peak, where the curve is highest, are more likely than values farther away, where the curve is closer to the horizontal axis.

Normal distributions appear in situations where there are a large number of independent but similar random events occurring. Things like heights of people in a particular population tend to roughly follow a normal distribution.