# Standard Deviation And Variance Pdf

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*In statistics , the standard deviation is a measure of the amount of variation or dispersion of a set of values. The standard deviation of a random variable , sample , statistical population , data set , or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust , than the average absolute deviation.*

- STATISTICS AND STANDARD DEVIATION Statistics and Standard Deviation
- Common menu bar links
- 4.2 Mean or Expected Value and Standard Deviation
- 2.8 – Expected Value, Variance, Standard Deviation

## STATISTICS AND STANDARD DEVIATION Statistics and Standard Deviation

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please contact us to request a format other than those available. Unlike range and quartiles, the variance combines all the values in a data set to produce a measure of spread. The variance symbolized by S 2 and standard deviation the square root of the variance, symbolized by S are the most commonly used measures of spread. We know that variance is a measure of how spread out a data set is. It is calculated as the average squared deviation of each number from the mean of a data set.

Measures of central tendency mean, median and mode provide information on the data values at the centre of the data set. Measures of dispersion quartiles, percentiles, ranges provide information on the spread of the data around the centre. In this section we will look at two more measures of dispersion called the variance and the standard deviation. The variance of the data is the average squared distance between the mean and each data value. It might seem strange that it is written in squared form, but you will see why soon when we discuss the standard deviation.

## Common menu bar links

Measures of central tendency mean, median and mode provide information on the data values at the centre of the data set. Measures of dispersion quartiles, percentiles, ranges provide information on the spread of the data around the centre. In this section we will look at two more measures of dispersion called the variance and the standard deviation. The variance of the data is the average squared distance between the mean and each data value. It might seem strange that it is written in squared form, but you will see why soon when we discuss the standard deviation. It has squared units. For example, the variance of a set of heights measured in centimetres will be given in centimeters squared.

## 4.2 Mean or Expected Value and Standard Deviation

Previous: 2. Next: 2. Analogous to the discrete case, we can define the expected value, variance, and standard deviation of a continuous random variable. These quantities have the same interpretation as in the discrete setting.

This means that over the long term of doing an experiment over and over, you would expect this average. If you repeat this experiment toss three fair coins a large number of times, the expected value of X is the number of heads you expect to get for each three tosses on average. It represents the mean of a population.

In statistics, the range is a measure of the total spread of values in a quantitative dataset. Unlike other more popular measures of dispersion, the range actually measures total dispersion between the smallest and largest values rather than relative dispersion around a measure of central tendency. The range is interpreted as t he overall dispersion of values in a dataset or, more literally, as the difference between the largest and the smallest value in a dataset. The range is measured in the same units as the variable of reference and, thus, has a direct interpretation as such. This can be useful when comparing similar variables but of little use when comparing variables measured in different units.

*Measures of central tendency mean, median and mode provide information on the data values at the centre of the data set. Measures of dispersion quartiles, percentiles, ranges provide information on the spread of the data around the centre.*

### 2.8 – Expected Value, Variance, Standard Deviation

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