standard deviation
nounDefinition of standard deviation
Examples of standard deviation in a Sentence
Recent Examples on the Web
Matthew Kraft, an educational economist at Brown University, has reviewed almost 800 randomized controlled trials of education interventions and found a median effect size of 0.1 standard deviation on student achievement outcomes. — Lydia Denworth, Scientific American, "Debate Arises over Teaching “Growth Mindsets” to Motivate Students," 12 Aug. 2019 Manfred may be talk of the coefficient of restitution, standard deviation, flow visualization and other scientific concepts when publicly addressing the scientific findings. — Josh Peter, USA TODAY, "These scientists may have solved MLB's 'juiced' baseball problem," 2 Aug. 2019 In our case, the growth rate of the populations has a different value each generation, distributed around the mean, with 99.7 percent of these values within three standard deviations of the mean. — Quanta Magazine, "Solution: ‘Why Are There Two Sexes?’," 28 July 2017 The effect is significant: The increase of one standard deviation in student debt translated into a decrease of 70 new small businesses per county — a decline of approximately 14.4 percent. — Washington Post, "7 ways $1.6 trillion in student loan debt affects the U.S. economy," 26 June 2019 In rare cases, the values can range even further away from the mean, and this is where the fatal flaw comes into play when the standard deviation is high: the value can reach zero, which implies extinction. — Quanta Magazine, "Solution: ‘Why Are There Two Sexes?’," 28 July 2017 The average African-American admitted to UNC has combined SAT scores 200 points (on a 1,600-point scale) below those of the average admitted Asian-American student—over a standard deviation of difference. — Heather Mac Donald, WSJ, "Diversity Delusions at North Carolina," 10 Feb. 2019 The most extreme spikes—those 10 standard deviations above the mean or more—skewed even more positive. — Andrea Fuller, WSJ, "How Companies Secretly Boost Their Glassdoor Ratings," 22 Jan. 2019 The difference between tutoring and traditional instruction after just three weeks was two standard deviations—to researchers, a truly incredible result. — Matt Barnum, The Atlantic, "The Outdated Study That Education Reformers Keep Citing," 30 Jan. 2018These example sentences are selected automatically from various online news sources to reflect current usage of the word 'standard deviation.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.
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More Definitions for standard deviation
standard deviation
nounFinancial Definition of standard deviation
What It Is
Standard deviation is a measure of how much an investment's returns can vary from its average return. It is a measure of volatility and in turn, risk. The formula for standard deviation is:
Standard Deviation = [1/n * (ri - rave)2]½
where:
ri = actual rate of return
rave = average rate of return
n = number of time periods
For math-oriented readers, standard deviation is the square root of the variance.
How It Works
Let's assume that you invest in Company XYZ stock, which has returned an average 10% per year for the last 10 years. How risky is this stock compared to, say, Company ABC stock? To answer this, let's first take a closer look at the year-by-year returns that compose that average:
At first look, we can see that the average return for both stocks over the last 10 years was indeed 10%. But let's look in a different way at how close XYZ's returns in any given year were to the average 10%:
As you can see, only during year 9 did XYZ return the average 10%. In the other years, the return was higher or lower -- sometimes much higher (as in year 7) or much lower (as in year 2). Now look at the annual returns on Company ABC stock, which also had a 10% average return for the last 10 years:
As you can see, Company ABC also averaged 10% return over 10 years but did so with far less variance than Company XYZ. Its returns are more tightly clustered around that 10% average. Thus, we can say that Company XYZ is more volatile than Company ABC stock. Standard deviation seeks to measure this volatility by calculating how "far away" the returns tend to be from the average over time.
For instance, let's calculate the standard deviation for Company XYZ stock. Using the formula above, we first subtract each year's actual return from the average return, then square those differences (that is, multiply each difference by itself):
Next, we add up column D (the total is 3,850). We divide that number by the number of time periods minus one (10-1=9; this is called the "nonbiased" approach and it is important to remember that some calculate standard deviation using all time periods -- 10 in this case rather than 9). Then we take the square root of the result. It looks like this:
Standard deviation = √(3,850/9) = √427.78 = 0.2068
Using the same process, we can calculate that the standard deviation for the less volatile Company ABC stock is a much lower 0.0129.
Why It Matters
Standard deviation is a measure of risk that an investment will not meet the expected return in a given period. The smaller an investment's standard deviation, the less volatile (and hence risky) it is. The larger the standard deviation, the more dispersed those returns are and thus the riskier the investment is.
Many technical indicators, such as Bollinger Bands, incorporate the notion of standard deviation as a way to determine whether to buy or sell a stock, but it is important to remember that standard deviation is only one of many measures of risk and should not be the last word in deciding whether a stock is "too risky" or "not risky enough."
Source: Investing Answers