The square values are then added together, giving a total of 11, which is then divided by the value of N minus 1, which is 3, resulting in a variance of approximately 3.67. denotes the sample mean: Since the Yi are selected randomly, both Galton was a keen observer. number of observations. deviation, the mean is assumed to have the normalization factor the only difference is that in step 1 we were calculating the average of the original numbers (10, 20, 30, 40, 50), but now in step 4 we are calculating the average of the squared deviations. is the covariance, which is zero for independent random variables (if it exists). is discrete with probability mass function ] The size of M in this dimension However, one can estimate the standard deviation of the entire population from the sample, and thus obtain an estimate for the standard error of the mean. i n ) , X ) length reduces to 1. The standard deviation is the square root of the variance. N scalar observations and weighting scheme A large dispersion shows how much the return on the fund is deviating from the expected normal returns. For other numerically stable alternatives, see Algorithms for calculating variance. x {\displaystyle V(X)} ) x ( Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. For each number in the set, we subtract the mean from that number. . In other words, investors should expect a higher return on an investment when that investment carries a higher level of risk or uncertainty. = In general, for the sum of [16][17][18], Samuelson's inequality is a result that states bounds on the values that individual observations in a sample can take, given that the sample mean and (biased) variance have been calculated. For instance, 1 signifies 1 standard deviation away from the mean, and so on. or 2 [ Unlike in the case of estimating the population mean, for which the sample mean is a simple estimator with many desirable properties (unbiased, efficient, maximum likelihood), there is no single estimator for the standard deviation with all these properties, and unbiased estimation of standard deviation is a very technically involved problem. ) 1 vectors. The standard deviation of a population or sample and the standard error of a statistic (e.g., of the sample mean) are quite different, but related. then they are said to be uncorrelated. c 1 {\displaystyle c^{\mathsf {T}}X} Thus, for a constant c and random variables X and Y: The standard deviation of the sum of two random variables can be related to their individual standard deviations and the covariance between them: where Standard deviations have an array of practical uses, most notably linked to statistics and measurements, which is why this online tool is in our "Statistics" category. F Kenney, John F.; Keeping, E.S. Standard deviation is a statistical measurement in finance that, when applied to the annual rate of return of an investment, sheds light on that investment's historical volatility. and If you do not specify the dimension, By calculating the standard deviation and understanding your low likelihood of actually averaging 10% in any single given year, you're better armed to make informed decisions and recognizing underlying risk. ( x Y L You can easily calculate variance and standard deviation, as well as skewness, kurtosis, percentiles, and other measures, using the Descriptive Statistics Excel Calculator. M In this tutorial we were calculating population variance and standard deviation. WebThe standard deviation of a sample is one of the most commonly cited descriptive statistics, explaining the degree of spread around a samples central tendency (the mean or median). Mathematically it is the average squared difference between each occurrence (each value) and the mean of the whole data set. 1 {\displaystyle s^{2}} This page is a step-by-step guide to calculating variance and standard deviation. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation. x [citation needed] It is because of this analogy that such things as the variance are called moments of probability distributions. Squaring the difference in each period and taking the average gives the overall variance of the return of the asset. becomes S WebStandard deviation has units that are the same as the units for the data values. , the variance becomes: These results lead to the variance of a linear combination as: If the random variables For this reason, describing data sets via their standard deviation or root mean square deviation is often preferred over using the variance. For example, arithmetic average of the numbers 10, 20, 30, 40, 50 is 10+20+30+40+50 (which is 150) divided by the count of numbers (which is 5). {\displaystyle X_{1},\dots ,X_{N}} For example, if X and Y are uncorrelated and the weight of X is two times the weight of Y, then the weight of the variance of X will be four times the weight of the variance of Y. n 2.1. exists, then, The conditional expectation ( since { The Cartoon Introduction to Statistics. {\displaystyle \sigma _{1}} {\displaystyle S^{2}} , {\displaystyle \operatorname {E} \left[(X-\mu )^{\operatorname {T} }(X-\mu )\right]=\operatorname {tr} (C),} If A is a , 1 is equal to A. + n If A is a vector of observations, then {\displaystyle \ell \in \mathbb {R} } Our stdev calculator also calculates the variance for you. The third population has a much smaller standard deviation than the other two because its values are all close to 7. After entering your data, use the STDEV.S formula if your data set is numeric or the STDEVA when you want to include text or logical values. S is a row vector containing the standard mean of A. ( Historical returns for Apples stock were 12.49% for 2016, 48.45% for 2017, -5.39% for 2018, 88.98% for 2019 and, as of September, 60.91% for 2020. then std(A) returns an array of zeros the same ] Standard deviation is calculated by taking the square root of a value derived from comparing data points to a collective mean of a population. 1 ( ) If A is a scalar, then M The estimator is a function of the sample of n observations drawn without observational bias from the whole population of potential observations. In this example, 34.1% of the data occurs within a range of 1 standard deviation from the The Hypothetical Growth of $10,000 chart reflects a hypothetical $10,000 investment and assumes reinvestment of dividends and capital gains. Consider an investment option with an average annual return of 10% per year. x 3 Then 2 For other uses, see, Distribution and cumulative distribution of, Addition and multiplication by a constant, Matrix notation for the variance of a linear combination, Sum of correlated variables with fixed sample size, Sum of uncorrelated variables with random sample size, Product of statistically dependent variables, Relations with the harmonic and arithmetic means, Montgomery, D. C. and Runger, G. C. (1994), Mood, A. M., Graybill, F. A., and Boes, D.C. (1974). , sample about its mean. MathWorldA Wolfram Web Resource. N If A is a matrix whose columns are random 0.025 The expression above can be extended to a weighted sum of multiple variables: If two variables X and Y are independent, the variance of their product is given by[10], Equivalently, using the basic properties of expectation, it is given by. X {\displaystyle X.} , R S = std(A,w,"all") X {\displaystyle L} This expression can be used to calculate the variance in situations where the CDF, but not the density, can be conveniently expressed. 2 1 0. WebStandard deviation is a statistic that measures the dispersion of a dataset, relative to its mean. Standard deviation is a term in statistics and probability theory used to quantify the amount of dispersion in a numerical data set, that is - how far from the normal (average) are the data points of interest. WebS = std(A,w) specifies a weighting scheme. beforehand. is the p-th quantile of the chi-square distribution with k degrees of freedom, and returns the standard deviation along dimension dim. n Netcials. The formula states that the variance of a sum is equal to the sum of all elements in the covariance matrix of the components. {\displaystyle n{S_{x}}^{2}+n{\bar {X}}^{2}} C She is the CEO of Xaris Financial Enterprises and a course facilitator for Cornell University. X This means that most men (about 68%, assuming a normal distribution) have a height within 3inches of the mean (6773inches) one standard deviation and almost all men (about 95%) have a height within 6inches of the mean (6476inches) two standard deviations. array or weight vector. 1 {\displaystyle \textstyle (x_{1}-{\bar {x}},\;\dots ,\;x_{n}-{\bar {x}}).}. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. x is the transpose of Define , and the conditional variance The variance is determined by subtracting the mean's value from each data point, resulting in -0.5, 1.5, -2.5, and 1.5. ( Non-normality makes testing for the equality of two or more variances more difficult. [ If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Standard Deviation Calculator", [online] Available at: https://www.gigacalculator.com/calculators/standard-deviation-calculator.php URL [Accessed Date: 11 Dec, 2022]. Firstly, if the true population mean is unknown, then the sample variance (which uses the sample mean in place of the true mean) is a biased estimator: it underestimates the variance by a factor of (n1) / n; correcting by this factor (dividing by n1 instead of n) is called Bessel's correction. Using the linearity of the expectation operator and the assumption of independence (or uncorrelatedness) of X and Y, this further simplifies as follows: In general, the variance of the sum of n variables is the sum of their covariances: (Note: The second equality comes from the fact that Cov(Xi,Xi) = Var(Xi).). The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. {\displaystyle \sigma } The standard deviation of two data sets can be combined using a specific combined standard deviation formula. This is, however, a hotly debated issue with many prominent financial practitioners denouncing the equation of risk and standard deviation. Taking square roots reintroduces bias (because the square root is a nonlinear function which does not commute with the expectation, i.e. X , ) N ( That is, it always has the same value: If a distribution does not have a finite expected value, as is the case for the Cauchy distribution, then the variance cannot be finite either. ) {\displaystyle c^{\mathsf {T}}} In the case where X takes random values from a finite data set x1, x2, , xN, with each value having the same probability, the standard deviation is, If, instead of having equal probabilities, the values have different probabilities, let x1 have probability p1, x2 have probability p2, , xN have probability pN. 1 X WebQuestia. tr A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard deviation is more commonly reported as a measure of dispersion once the calculation is finished. There are cases when a sample is taken without knowing, in advance, how many observations will be acceptable according to some criterion. is a vector- and complex-valued random variable, with values in an m-by-1 column ) , it is found that the distribution, when both causes act together, has a standard deviation Create a 3-D array and compute the standard deviation over each page of data (rows and columns). N1 corresponds to the number of degrees of freedom in the vector of deviations from the mean, Standard deviation is calculated as the square root of the variance, while the variance itself is the average of the squared differences from the arithmetic mean. x = These same formulae can be used to obtain confidence intervals on the variance of residuals from a least squares fit under standard normal theory, where k is now the number of degrees of freedom for error. Therefore, standard deviation is often considered a more robust, accurate measurement compared to other observations. Weigh by difference approximately 0.40 -0.50 g of unknown into each of three separate clean 250 mL Erlenmeyer flasks. {\displaystyle \mu =\operatorname {E} (X)} 5.024 becomes 1 while the sizes of all other Find out how you can explore your interests and build skills to make your mark on the world with a UMass education. If the mean is determined in some other way than from the same samples used to estimate the variance then this bias does not arise and the variance can safely be estimated as that of the samples about the (independently known) mean. Standard deviation is important because it can help users assess risk. All those values are then squared to yield 8.2%, 0.54%, 21.6%, 22.93%, and 3.93%. where As another example, the population {1000, 1006, 1008, 1014} may represent the distances traveled by four athletes, measured in meters. The graph below illustrates the point by comparing two distributions of 18 elements each, with different standard deviations (2.26 and 8.94): You can check the numbers in the data sets and the resulting calculations in our SD calculator here for set 1 and here for set 2. satisfies std(A) operates along the first array dimension whose This function fully supports GPU arrays. For historical volatility of stocks and other assets, you can use the Historical Volatility Calculator. The lengths of the output {\displaystyle X} computes the standard deviation over all elements in A, since Population and sampled standard deviation calculator. X ( {\displaystyle \mathbb {V} (X)} = When evaluating investments, investors should estimate both the expected return and the uncertainty of future returns. containing the standard deviation corresponding to each column. , M. If a weighting scheme is specified, then For . The proportion that is less than or equal to a number, x, is given by the cumulative distribution function: If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean (mathematically, , where is the arithmetic mean), about 95 percent are within two standard deviations (2), and about 99.7 percent lie within three standard deviations (3). Unlike the expected absolute deviation, the variance of a variable has units that are the square of the units of the variable itself. while the sizes of all other dimensions are the same as 1 Springer-Verlag, New York. , , , A volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low. = , [ 5 You have a modified version of this example. WebAround 68% of values are within 1 standard deviation of the mean. 1 A lower standard deviation isn't necessarily preferable. N In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. w is either 0 or 1. n std returns the weighted ( is referred to as the biased sample variance. {\displaystyle {\frac {1}{N}}} ( 4 {\displaystyle n} WebAround 68% of values are within 1 standard deviation of the mean. A low standard deviation means that the data points are clustered around the sample mean while a high SD indicates that the set of data is spread over a wide range of values. 1 For example, assume an investor had to choose between two stocks. S 6 In this example that sample would be the set of actual measurements of yesterday's rainfall from available rain gauges within the geography of interest. In such cases, the sample size N is a random variable whose variation adds to the variation of X, such that. In the next step we need to calculate the deviations from the mean. b Our online calculators, converters, randomizers, and content are provided "as is", free of charge, and without any warranty or guarantee. S This can easily be proven with (see basic properties of the variance): In order to estimate the standard deviation of the mean which is the trace of the covariance matrix. If there is only one observation, then 2 If A is a Y By definition (and due to the way arithmetic mean is calculated as sum of values divided by count of values), the sum (and therefore also the average) of all deviations from arithmetic mean for any set of data must be zero, because the positive and negative deviations cancel each other. This syntax is valid for MATLAB versions R2022a and later. One can find the standard deviation of an entire population in cases (such as standardized testing) where every member of a population is sampled. Therefore, the variance of the mean of a large number of standardized variables is approximately equal to their average correlation. which means that the standard deviation is equal to the square root of the difference between the average of the squares of the values and the square of the average value. In the case that Yi are independent observations from a normal distribution, Cochran's theorem shows that S2 follows a scaled chi-squared distribution (see also: asymptotic properties):[13], If the Yi are independent and identically distributed, but not necessarily normally distributed, then[15]. array, then std(A) returns NaN. M is a scalar. {\displaystyle \sigma ^{2}} Correcting for this bias yields the unbiased sample variance, denoted To be more certain that the sampled SD is close to the actual SD we need to sample a large number of points. On the basis of risk and return, an investor may decide that Stock A is the safer choice, because Stock B's additional two percentage points of return is not worth the additional 10 pp standard deviation (greater risk or uncertainty of the expected return). This estimator is commonly used and generally known simply as the "sample standard deviation". A small population of N = 2 has only 1 degree of freedom for estimating the standard deviation. {\displaystyle \sigma _{\text{mean}}} For example, if a series of 10 measurements of a previously unknown quantity is performed in a laboratory, it is possible to calculate the resulting sample mean and sample standard deviation, but it is impossible to calculate the standard deviation of the mean. The calculation of the sum of squared deviations can be related to moments calculated directly from the data. {\displaystyle P} Around 99.7% of values are within 3 standard deviations of the mean. This always consists of scaling down the unbiased estimator (dividing by a number larger than n1), and is a simple example of a shrinkage estimator: one "shrinks" the unbiased estimator towards zero. with corresponding probabilities . Statistical tests such as these are particularly important when the testing is relatively expensive. {\displaystyle \operatorname {E} (X\mid Y)=g(Y). + , or sometimes as of Standard deviation is calculated as the square root of the variance. Estimating the population variance by taking the sample's variance is close to optimal in general, but can be improved in two ways. given by. erf {\displaystyle X} vecdim when w is 0 or 1. size as A. Vector of dimensions, specified as a vector of positive integers. X . It measures the accuracy with which a sample represents a population. = It compares each data point to the mean of all data points, and standard deviation returns a calculated value that describes whether the data points are in close proximity or whether they are spread out. X The data set lists values for each of the variables, such as for example height and denotes the transpose of where {\displaystyle Q_{1}=0} constant. ( The bias in the variance is easily corrected, but the bias from the square root is more difficult to correct, and depends on the distribution in question. You can learn more about the standards we follow in producing accurate, unbiased content in our, The sum of squares is a statistical technique used in regression analysis. ( When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population). When variance is calculated from observations, those observations are typically measured from a real world system. Now we have the squared deviations from the mean almost the whole definition of variance. , ( is the mean value of these observations, while the denominatorN stands for the size of the sample: this is the square root of the sample variance, which is the average of the squared deviations about the sample mean. Calculate with arrays that have more rows than fit in memory. 1 [7] However, this is a biased estimator, as the estimates are generally too low. Let be the expected value (the average) of random variable X with density f(x): Using words, the standard deviation is the square root of the variance of X. Calculate the variance for each data point. X = There is only one part left: the word average. {\displaystyle k-1=0} x More aggressive investors may be comfortable with an investment strategy that opts for vehicles with higher-than-average volatility, while more conservative investors may not. where ymax is the maximum of the sample, A is the arithmetic mean, H is the harmonic mean of the sample and is the expected value. Stock A over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points (pp) and Stock B, over the same period, had average returns of 12 percent but a higher standard deviation of 30 pp. x {\displaystyle L} Each test statistic has a similar function that statistics programs use to estimate the probability of. ( ) The excess kurtosis may be either known beforehand for certain distributions, or estimated from the data.[9]. Where: For three or more groups, change the 2 in the denominator to reflect the number of samples, k: S ) arrays. N Var .[8]. values: "includenan" Include f How Is Standard Deviation Used to Determine Risk? k Schaums Easy Outline of Statistics, Second Edition (Schaums Easy Outlines) 2nd Edition. Finding the square root of this variance will give the standard deviation of the investment tool in question. X Arranging the squares into a rectangle with one side equal to the number of values, This page was last edited on 24 October 2022, at 11:16. Cohen (1988) offers a couple of options for calculating the pooled standard deviation. Example - 5 Variance and Standard Deviation for Grouped Data. Check out our Practically Cheating Calculus Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book. [ The standard deviation will be larger, and it is relatively more affected by larger values. 2 For each period, subtracting the expected return from the actual return results in the difference from the mean. S = std(A,w) , and Learn how to calculate the sum of squares and when to use it. Then we divide 1,000 by 5 and get 200. for some X (pronounced "sigma squared"). X ) M is a row vector containing the mean If the conditions of the law of large numbers hold for the squared observations, S2 is a consistent estimator of2. If A is a multidimensional array, then p Standard deviation is all-inclusive of observations. ( i Secondly, squaring gives much bigger weight to big numbers (or big negative numbers) than to numbers close to zero. 3 , 0 N instead of N 1. The term variance was first introduced by Ronald Fisher in his 1918 paper The Correlation Between Relatives on the Supposition of Mendelian Inheritance:[2]. As a downside, the standard deviation calculates all uncertainty as risk, even when its in the investor's favorsuch as above-average returns. . , then. n X {\displaystyle X_{1},\dots ,X_{N}} {\displaystyle \alpha \in (1,2]} < [ {\displaystyle E[{\sqrt {X}}]\neq {\sqrt {E[X]}}} In statistical inference through null-hypothesis statistical tests the procedure is to establish what the expected distribution of outcomes from a test is, assuming a set of conditions are true, and then compare the actually observed data (converted to standard deviation measures) to that expected outcome. {\displaystyle x} {\displaystyle {\tilde {S}}_{Y}^{2}} r {\displaystyle X} WebExample Calculating the Standard Deviation for Weight Data. "omitnat" Ignore {\displaystyle \textstyle \operatorname {cov} } ( , then in the formula for total variance, the first term on the right-hand side becomes, where N. For a finite-length vector A made up of {\displaystyle {\mathit {SS}}} Standard deviation is the square root of variance. E Enter probability or weight and data number in each row: Data number: Probability , Marshall Hargrave is a stock analyst and writer with 10+ years of experience covering stocks and markets, as well as analyzing and valuing companies. 32 N Different practical situations require different thresholds (levels of statistical significance), which can be expressed in terms of standard deviations, say 2 standard deviations from the expected, or in terms of percentage probability of the observation under the null: 5%, 1%, etc. Particle physics conventionally uses a standard of "5 sigma" for the declaration of a discovery. Y An approximation can be given by replacing N1 with N1.5, yielding: The error in this approximation decays quadratically (as 1/N2), and it is suited for all but the smallest samples or highest precision: for N = 3 the bias is equal to 1.3%, and for N = 9 the bias is already less than 0.1%. E The second moment of a random variable attains the minimum value when taken around the first moment (i.e., mean) of the random variable, i.e. 0.975 The most commonly used value for n is 2; there is about a five percent chance of going outside, assuming a normal distribution of returns. Part II - Percentage purity of KHP Repeat the experiment with unknown samples. The wider the curve's width, the larger a data set's standard deviation from the mean. Investment firms report the standard deviation of their mutual funds and other products. : Either estimator may be simply referred to as the sample variance when the version can be determined by context. If A is a 0-by-0 ( where f 2 If the distribution has fat tails going out to infinity, the standard deviation might not exist, because the integral might not converge. Risk is an important factor in determining how to efficiently manage a portfolio of investments because it determines the variation in returns on the asset and/or portfolio and gives investors a mathematical basis for investment decisions (known as mean-variance optimization). If the biased sample variance (the second central moment of the sample, which is a downward-biased estimate of the population variance) is used to compute an estimate of the population's standard deviation, the result is. If A is a scalar, then S is ( Assuming statistical independence of the values in the sample, the standard deviation of the mean is related to the standard deviation of the distribution by: where N is the number of observations in the sample used to estimate the mean. M Co-efficient of variation (CV) is a measure of the dispersion of data points around the mean in a series. Variance is the. ) The standard deviation is more amenable to algebraic manipulation than the expected absolute deviation, and, together with variance and its generalization covariance, is used frequently in theoretical statistics; however the expected absolute deviation tends to be more robust as it is less sensitive to outliers arising from measurement anomalies or an unduly heavy-tailed distribution. {\displaystyle \mathbb {C} ,} When w = 1, the standard deviation is be the covariance matrix of In two dimensions, the standard deviation can be illustrated with the standard deviation ellipse (see Multivariate normal distribution Geometric interpretation). , random variables X X ( , std is operating. The sample standard deviation can be computed as: For a finite population with equal probabilities at all points, we have. You can use a n Practice Problem 4: Manufacturing. When the values xi are weighted with unequal weights wi, the power sums s0, s1, s2 are each computed as: And the standard deviation equations remain unchanged. x If A is a matrix whose columns are random is the average value. Standard deviation may serve as a measure of uncertainty. The square root is a concave function and thus introduces negative bias (by Jensen's inequality), which depends on the distribution, and thus the corrected sample standard deviation (using Bessel's correction) is biased. [4][5] Roughly, the reason for it is that the formula for the sample variance relies on computing differences of observations from the sample mean, and the sample mean itself was constructed to be as close as possible to the observations, so just dividing by n would underestimate the variability. S WebIn 2000 the mean weight of 10 year olds was found to be \(27\,kg\) and the standard deviation was 3.5. {\displaystyle \{X_{1},\dots ,X_{N}\}} {\displaystyle X^{\operatorname {T} }} Population standard deviation of grades of eight students, Standard deviation of average height for adult men, Confidence interval of a sampled standard deviation, Experiment, industrial and hypothesis testing, Relationship between standard deviation and mean, Unbiased estimation of standard deviation, unbiased estimation of standard deviation, Variance Distribution of the sample variance, Student's t-distribution Robust parametric modeling, Multivariate normal distribution Geometric interpretation, "CERN experiments observe particle consistent with long-sought Higgs boson | CERN press office", "On the dissection of asymmetrical frequency curves", Philosophical Transactions of the Royal Society A, "Earliest Known Uses of Some of the Words of Mathematics", Multivariate adaptive regression splines (MARS), Autoregressive conditional heteroskedasticity (ARCH), https://en.wikipedia.org/w/index.php?title=Standard_deviation&oldid=1120954441, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 9 November 2022, at 18:42. std(A,0,[1 2]) returns a 1-by-1-by-3 array whose N Data Types: single | double | datetime | duration On the other hand, one can expect aggressive growth funds to have a high standard deviation from relative stock indices, as their portfolio managers make aggressive bets to generate higher-than-average returns. + The summation is for the standard i=1 to i=n sum. x n Many analysts are probably more familiar with standard deviation than compared to other statistical calculations of data deviation. By default, the standard deviation is normalized by {\displaystyle X} i E in the specified operating dimensions are 1, while the others remain the {\displaystyle N>75} We sum them up and get 1,000. After more than twenty years, Questia is discontinuing operations as of Monday, December 21, 2020. When there are two independent causes of variability capable of producing in an otherwise uniform population distributions with standard deviations In linear regression analysis the corresponding formula is. For where C X Our standard deviation calculator supports both formulas with the flip of a switch. {\displaystyle c} variables and whose rows are observations, then For example, a volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low. 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