{"id":30311,"date":"2024-10-29T11:21:59","date_gmt":"2024-10-29T11:21:59","guid":{"rendered":"https:\/\/www.editage.com\/insights-new\/?p=30311"},"modified":"2026-03-12T11:06:13","modified_gmt":"2026-03-12T05:36:13","slug":"what-is-standard-deviation-and-how-to-find-standard-deviation","status":"publish","type":"post","link":"https:\/\/www.editage.com\/insights\/what-is-standard-deviation-and-how-to-find-standard-deviation","title":{"rendered":"What is standard deviation and how to find standard deviation"},"content":{"rendered":"

When you\u2019re summarizing large amounts of data as a researcher, you\u2019re using summary statistics or descriptive statistics<\/a>. And the most popular among these is the mean or average. But a mean by itself is \u201cmean\u201dingless without the standard deviation. So, let\u2019s understand this important statistic today.<\/p>\n

What is standard deviation? <\/strong><\/h2>\n

Standard deviation (SD) is a measure of dispersion. It tells you how widely the values are dispersed (i.e., vary) from the mean.<\/p>\n

If SD is small, there\u2019s less variation in the values, and they fall into a fairly narrow range around the mean. A very large SD implies that there\u2019s a lot of variation in your data.<\/p>\n

How to find standard deviation: Calculations and formula <\/strong><\/h2>\n

This is pretty simple, if you follow the steps below:<\/p>\n

Step 1: Collect data (e.g., systolic blood pressure readings)<\/p>\n

Step 2: Calculate the mean. To do so, add up all the data values and divide by the total number of data points.<\/p>\n

Step 3: Subtract the mean from each data point in order to get the Deviation.<\/p>\n

Step 4: Square each deviation (so that you remove any negative values).<\/p>\n

Step 5: Calculate the mean of the squared deviations. This is called Variance.<\/p>\n

Step 6: Find the square root of the variance. This is your Standard Deviation.<\/p>\n

How to report standard deviation: Symbol or abbreviation? <\/strong><\/h2>\n

SD is sometimes denoted using the \u00b1 sign, but that\u2019s not strictly necessary because SD by definition implies \u201cplus or minus\u201d (variation on both sides of the mean). It can also cause confusion about whether the number is a standard deviation or standard error of the mean (more on that below).<\/p>\n

So, the ideal format to report standard deviation is<\/p>\n

Mean = 13.5 (SD = 1.3)<\/p>\n

Of course, you must adhere to the style guide set by your own journal (\u201cSD\u201d vs \u201cs.d.\u201d vs \u201csd\u201d, etc.). And remember, if you\u2019re reporting more than one mean, each mean must have its corresponding SD.<\/p>\n

Standard deviation versus standard error of the mean <\/strong><\/h2>\n

Researchers sometimes confuse standard deviation with standard error of the mean (SEM). The latter is actually a measure of precision. It tells you how close your sample mean is to the population mean. SEM doesn\u2019t tell you about the variation in the data. Check out Lee et al. (2015)\u2019s<\/a> helpful article on the differences between SD and SEM.<\/p>\n

SEM is often misused as a substitute for SD<\/a>, because its values are typically smaller than those of SD.<\/p>\n

For this reason, many biostatisticians (e.g., Barde & Barde, 2012<\/a>; Garg & Mohanty, 2012<\/a>; Ko et al., 2014)<\/a> and journals discourage authors from reporting SEM along with means when describing their data. Journals like Nature Communications<\/a> and Obstetrics & Gynecology Science<\/a> ask authors to clearly identify whether a measure is SD or SEM.<\/p>\n

Standard deviation vs variance <\/strong><\/h2>\n

As you saw earlier, one of the steps in calculating SD is to calculate Variance (Step 5). Variance and SD are not the same. SD is the square root of variance for a dataset.<\/p>\n

SD and variance also serve different purposes:<\/p>\n

SD: quantifies how far data points are from the mean<\/p>\n

Variance: measures the spread between numbers in a dataset<\/p>\n

We hope this guide helped you in understanding standard deviation and its importance in research. Here, we have summarized the definition, calculation methods and reporting of standard deviation.<\/p>\n

\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

When you\u2019re summarizing large amounts of data as a researcher, you\u2019re using summary statistics or descriptive statistics. And the most popular among these is the mean or average. But a mean by itself is \u201cmean\u201dingless without the standard deviation. So, let\u2019s understand this important statistic today. What is standard deviation? Standard deviation (SD) is a […]<\/p>\n","protected":false},"author":15,"featured_media":30312,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2420],"tags":[2622,1319,366],"new_categories":[],"new_tags":[],"series":[],"class_list":["post-30311","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-analysis","tag-analysisofdata","tag-statistical-analysis","tag-statistical-reporting"],"acf":[],"yoast_head":"\nStandard Deviation Guide for Researchers | Editage Insights<\/title>\n<meta name=\"description\" content=\"Learn the basics of standard deviation, how to calculate it and how to report it correctly in your research paper.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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