
Review of Short Phrases and Links 
This Review contains major "Standard Deviation" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 The standard deviation is the square root of the variance, or root mean square deviation from the mean, in either a population or a sample.
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 The standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are.
 The standard deviation is defined as the square root of the variance.
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 The standard deviation is the most commonly used measure of statistical dispersion.
 The standard deviation is the square root of the average of squared deviations from the mean.
 For a normal distribution, 1.4826· MAD can be used to estimate the standard deviation .
 For normal distributions, the two points of the curve which are one standard deviation from the mean are also the inflection points.
 Keep in mind that the standard deviation has a special relationship to the normal curve that helps in its interpretation.
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 The population standard deviation is 1.00; the sample standard deviation is 1.04.
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 The `I u S' (`calcvectorpopsdev') [`vpsdev'] command computes the *population* standard deviation.
 Previously, we showed how to compute the margin of error, based on the critical value and standard deviation.
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 This interval assumes there is only sampling error, a function of the confidence level, the population standard deviation, and the sample size.
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 Bthe population variance is represented by σ2, while s2 is the standard deviation.
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 For a normal population, the standard deviation can be estimated by dividing the interquartile range by 1.34898.
 Typical measures of spread are variance, standard deviation, range, and interquartile range.
 It is a symmetric distribution, shaped like a bell, and is completely determined by its mean and standard deviation.
 The result is that the geometric mean is calculated for you and a different kind of standard deviation is produced.
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 The standard deviation is usually more useful and better adapted to further analysis than the mean absolute deviation.
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 Standard Deviation Average amount the data deviates from the mean (average) of the data set.
 Univariate statistics include well known calculations such as the mean, median, mode, quartiles, variance, standard deviation, and skewness.
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 What if you were just starting out and collected 31 observations and had no prior knowledge of the mean, standard deviation, median, IQR or histogram.
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 One way of measuring this spread is by calculating the variance or the standard deviation of the data.
 Just as the mean and standard deviation can be distorted by extreme values in the tails, so too can the skewness and kurtosis measures.
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 This is because the standard deviation is more sensitive than the semiinterquartile range to extreme values.
 Said more formally, the standard deviation is the root mean square (RMS) deviation of values from their arithmetic mean.
 However, s is not an unbiased estimator for the standard deviation ; it tends to underestimate the population standard deviation.
 Standard deviation, being the square root of that quantity, therefore measures the spread of data about the mean, measured in the same units as the data.
 The standard deviation is always a positive number (or zero) and is always measured in the same units as the original data.
 For example, if one measured height in inches, then the standard deviation would be in inches, while the variance would be in inches squared.
 Keep in mind that variance s 2 measures the same thing as standard deviation s (dispersion of scores in a distribution).
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 The standard deviation of the sampling distribution of the mean is called the standard error of the mean.
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 The standard deviation of the sampling distribution is smaller than in the previous example because the size of each sample is larger.
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 In other words, it is the standard deviation of the sampling distribution of the sample statistic.
 For a probability distribution, the coefficient of variation is defined as the ratio of the standard deviation to the point estimate of the mean.
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 The sample standard deviation is the square root of the sample variance.
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 It can be expressed by the variance or the standard deviation.
 By default, the procedure estimates with the sample mean and with the sample standard deviation.
 The sample standard deviation is similar to the root mean square deviation, except that a divisor of n1 rather than n is used.
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 For example, the standard deviation of a random variable which follows a Cauchy distribution is undefined.
 Not all random variables have a standard deviation, since these expected values need not exist.
 If the random variable X takes on the values (which are real numbers) with equal probability, then its standard deviation can be computed as follows.
 Suppose again that X is a realvalued random variable for our basic experiment, with mean μ and standard deviation σ (assumed finite).
 In a loose sense, the standard deviation tells us how far from the mean the data points tend to be.
 To understand standard deviation, keep in mind that variance is the average of the squared differences between data points and the mean.
 We will show how to calculate the standard deviation of a population.
 In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean.
 A team that is consistently good in most categories will also have a low standard deviation and will therefore end up winning more than losing.
 So, a team that is consistently bad in most categories will have a low standard deviation indicating they will probably lose more often than win.
 The most common way to describe the range of variation is standard deviation (usually denoted by the Greek letter sigma: ).
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 The interval defined by the standard deviation is the 68.3% ("one sigma") confidence interval of the measurements.
 The confidence interval indicates that the population standard deviation lies between 28.1 and 37.2.
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 Approximate confidence interval for standard deviation of nonnormal distributions.
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 So, the standard deviation is the square root of five halves, or approximately 1.58.
 If the distribution is approximately normal or a symmetric bellshape, the classic measure of variation is the standard deviation.
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 The standard deviation is associated with the mean and is an accurate measure of spread for symmetric bellshaped distributions.
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 When the examples are pretty tightly bunched together and the bellshaped curve is steep, the standard deviation is small.
 This function computes the weighted skewness of the dataset data using the given values of the weighted mean and weighted standard deviation, wmean and wsd.
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 The mean, median TIT. mode, variance and standard deviation are descriptive statistics.
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 This is an example of using a descriptive statistic (standard deviation) for inferential purposes.
 Thus, multiplying Gini's mean difference by yields a robust estimator of the standard deviation when the data are from a normal sample.
 The coefficient of variation of a sample is the ratio of the standard deviation to the mean.
 In most cases, the standard deviation is estimated by examining a random sample taken from the population.
 The sample from school B has an average score of 950 with a standard deviation of 90.
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 A random sample of 100 children shows an average weight of 47 kg with a standard deviation of 8 kg.
 Standard deviation may serve as a measure of uncertainty.
 Both variance s 2 and standard deviation s measure variability within a distribution.
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 STANDARD DEVIATION. The most widely used measure of dispersion of a frequency distribution, equal to the positive square root of the variance.
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 An important characteristic of the standard deviation is as a measure of the percentile rank.
 If, for instance, the data set {0, 6, 8, 14} represents the ages of four siblings, the standard deviation is 5 years.
 The four most common measures of variation are the range, variance, standard deviation, and coefficient of variation.
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 The third set has a much smaller standard deviation than the other two because its values are all close to 7.
 Notice how the standard deviation on our dependent variable, science knowledge scores, gets smaller and smaller with each successive educational level.
 The mean and the standard deviation of a set of data are usually reported together.
 The aim is to produce a transformed data set with a mean of zero and a standard deviation of one.
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 If the mean and standard deviation of a normal distribution are known, it is easy to convert back and forth from raw scores to percentiles.
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 A bandwidth that minimizes AMISE can be derived by treating as the normal density having parameters and estimated by the sample mean and standard deviation.
 When referring to the population mean or standard deviation, the term parameter is used.
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