Recent Examples of standard deviation from the Web
The research team found that each one standard deviation increase in handgrip strength was associated with an increase in stroke volume, an increase in end-diastolic volume and a decrease in left ventricular mass.
For example, the researchers looked at patents from examiners whose average change in patent claim length was one standard deviation below average—suggesting that the claims in these patents had received below-average scrutiny.
Peter Margules decided to send his son, now 8, to Steppingstone School in Farmington Hills, Michigan, a school for academically exceptional students, after the child was discovered to have an IQ score that was two standard deviations above gifted.
Rondo has one of the highest standard deviations in the league for players in and around his average production.
To put this in technical terms, no other NBA team has a lower standard deviation in wins or end-of-season rankings this decade.
The only real question mark is Rondo, whose standard deviation of minutes is the thing of nightmares.
Experts suggest instead using one of these formulas: 208 - (0.7 x age) or 206.9 - (0.67 x age), both of which have standard deviations closer to 7.
That rate, a fifth of a standard deviation every decade, is about the same improvement as has been seen in IQ tests over the past 80 years.
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Financial 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
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."
Learn More about standard deviation
Britannica.com: Encyclopedia article about standard deviation
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