question: What exactly does the term Standard Deviation mean. I know it is a synonym for outlier but it it more? Thanks!
comment: Standard deviation is associated with outliers but it is not a synonym. Standard deviation refers to the "spread" of a data set. For example grades: if 90% of a class got a B and 5% got an A or C on an assignment the standard deviation would be small. If 10% got an F, 20% got a D, 40% got a C, 20% got a B, and 10% got an A then the standard deviation would be much larger than in the first example. Normally outliers are considered to be 2 standard deviations from the average (sometimes the average value of the data sometimes the middle/most common piece of the data). So if you had a bunch of data points who's average was 50 and standard deviation was 10 any data points below 50-2*10=30 or above 50+2*10=70 would be considered outliers.
passages: Section::::Basic examples.:Standard deviation of average height for adult men.
   In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the mean of the data set.
  
  where
  
  Section::::Measures.
  
  Section::::Measures.:Mean signed deviation.
   Section::::Interpretation and application.:Application examples.:Finance.
   Section::::Basic examples.:Population standard deviation of grades of eight students.
  
  Suppose that the entire population of interest was eight students in a particular class. For a finite set of numbers, the population standard deviation is found by taking the square root of the average of the squared deviations of the values subtracted from their average value. The marks of a class of eight students (that is, a statistical population) are the following eight values:
  
  These eight data points have the mean (average) of 5:
  
  First, calculate the deviations of each data point from the mean, and square the result of each:
   Section::::Assumptions and usage.:Standard error of mean versus standard deviation.
   and places where 1/"n" is used above must be replaced by "w"/"W":
  
  In the final division,
  
  and
  
  or 
  
  where "n" is the total number of elements, and "n"' is the number of elements with non-zero weights.
  
  The above formulas become equal to the simpler formulas given above if weights are taken as equal to one.
  
  Section::::History.
  
  The term "standard deviation" was first used in writing by Karl Pearson in 1894, following his use of it in lectures. This was as a replacement for earlier alternative names for the same idea: for example, Gauss used "mean error".
  
  Section::::See also.
   Standard deviation is often used to compare real-world data against a model to test the model.
   In those contexts where standard error of the mean is defined not as the standard deviation of the sample mean, but as its estimate, this is the estimate typically given as its value. Thus, it is common to see standard deviation of the mean alternatively defined as:
   For example, each of the three populations {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has a mean of 7. Their standard deviations are 7, 5, and 1, respectively. The third population has a much smaller standard deviation than the other two because its values are all close to 7. It will have the same units as the data points themselves. If, for instance, the data set {0, 6, 8, 14} represents the ages of a population of four siblings in years, the standard deviation is 5 years. As another example, the population {1000, 1006, 1008, 1014} may represent the distances traveled by four athletes, measured in meters. It has a mean of 1007 meters, and a standard deviation of 5 meters.
   A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
   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).
  
  Section::::Basic examples.
  
  Section::::Basic examples.:Sample standard deviation of metabolic rate of northern fulmars.
  
  Logan
  
  gives the following example. Furness and Bryant measured the resting metabolic rate for 8 male and 6 female breeding northern fulmars. The table shows the Furness data set.
   Deviation
  
  Deviation may refer to:
  
  Section::::Mathematics and engineering.
  
  BULLET::::- Allowance (engineering), an engineering and machining allowance is a planned deviation between an actual dimension and a nominal or theoretical dimension, or between an intermediate-stage dimension and an intended final dimension.
  
  BULLET::::- Deviation (statistics), the difference between the value of an observation and the mean of the population in mathematics and statistics
  
  BULLET::::- Standard deviation, which is based on the square of the difference
  
  BULLET::::- Absolute deviation, where the absolute value of the difference is used
   The relative standard error of a sample mean is the standard error divided by the mean and expressed as a percentage. It can only be calculated if the mean is a non-zero value.
   Section::::Standard error of the mean.:Population.
  
  The standard error of the mean (SEM) can be expressed as:
  
  where
  
  Section::::Standard error of the mean.:Population.:Estimate.
  
  Since the population standard deviation is seldom known, the standard error of the mean is usually estimated as the sample standard deviation divided by the square root of the sample size (assuming statistical independence of the values in the sample).
  
  where
  
  Section::::Standard error of the mean.:Sample.
   In the case of a parametric family of distributions, the standard deviation can be expressed in terms of the parameters. For example, in the case of the log-normal distribution with parameters "μ" and "σ", the standard deviation is
  
  Section::::Estimation.
   Section::::Definition of population values.
  
  Let "X" be a random variable with mean value "μ":
  
  Here the operator E denotes the average or expected value of "X". Then the standard deviation of "X" is the quantity
  
  (derived using the properties of expected value).
  
  In other words, the standard deviation "σ" (sigma) is the square root of the variance of "X"; i.e., it is the square root of the average value of ("X" − "μ").
   Section::::Brief history.
  
  The first rigorous results concerning large deviations are due to the Swedish mathematician Harald Cramér, who applied them to model the insurance business. From the point
   Standard score
  
  In statistics, the standard score is the signed fractional number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores. 
   Standard deviation may serve as a measure of uncertainty. In physical science, for example, the reported standard deviation of a group of repeated measurements gives the precision of those measurements. When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance: if the mean of the measurements is too far away from the prediction (with the distance measured in standard deviations), then the theory being tested probably needs to be revised. This makes sense since they fall outside the range of values that could reasonably be expected to occur, if the prediction were correct and the standard deviation appropriately quantified. See prediction interval.
   While the standard deviation does measure how far typical values tend to be from the mean, other measures are available. An example is the mean absolute deviation, which might be considered a more direct measure of average distance, compared to the root mean square distance inherent in the standard deviation.
  
  Section::::Interpretation and application.:Application examples.
  
  The practical value of understanding the standard deviation of a set of values is in appreciating how much variation there is from the average (mean).
  
  Section::::Interpretation and application.:Application examples.:Experiment, industrial and hypothesis testing.
   Financial risk is most commonly measured in terms of the variance or standard deviation of a quantity such as percentage returns or rates of change. In foreign exchange, a relevant factor would be the rate of change of the foreign currency spot exchange rate. A variance, or spread, in exchange rates indicates enhanced risk, whereas standard deviation represents exchange-rate risk by the amount exchange rates deviate, on average, from the mean exchange rate in a probabilistic distribution. A higher standard deviation would signal a greater currency risk. Because of its uniform treatment of deviations and for the automatically squaring of deviation values, economists have criticized the accuracy of standard deviation as a risk indicator. Alternatives such as average absolute deviation and semivariance have been advanced for measuring financial risk.
   The variance is the mean of these values:
  
  and the "population" standard deviation is equal to the square root of the variance:
   Core to any statistical analysis is the concept that measurements vary: they have both a central tendency, or mean, and a spread around this central value, or variance. In the late 1860s, Galton conceived of a measure to quantify normal variation: the standard deviation.
   In science, many researchers report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant—normal random error or variation in the measurements is in this way distinguished from likely genuine effects or associations. The standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.
   Section::::Formulation.
  
  Suppose that the data set consists of the points ("x", "y") with "i" = 1, 2, ..., "n". We want to find a function "f" such that formula_1
  