# Module on measures of variability

### The measure of variability that is influenced most by extreme values is

Learning Objectives Interpret the range as the overall dispersion of values in a dataset Key Takeaways Key Points 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. If you know only the mean, there will be many possible sets of data that are consistent with this model. For example, if all student users of the library were asked how many books they had borrowed in the past month then the entire population has been studied since all the students have been asked. Share this page:. One of the median's advantages is that it is not sensitive to outliers. Key Terms variation ratio: the proportion of cases not in the mode qualitative data: data centered around descriptions or distinctions based on some quality or characteristic rather than on some quantity or measured value The study of statistics generally places considerable focus upon the distribution and measure of variability of quantitative variables. Therefore, if you need to estimate an unknown population variance, based on data from a simple random sample, this is the formula to use.

In such a discussion, we would consider the variability of qualitative data in terms of unlikeability. If the dataset had the same mean of 25 but a larger standard deviation for example, 2.

Often they represent different properties of an individual statistical unit e. The inter-quartile range is found by subtracting the lower quartile from the upper quartile.

The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. If the mean is greater than the median, the distribution is said to be positively skewed.

## Measures of variability calculator

Unlike the estimation of 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. Quartiles divide an ordered data set into four equal parts. Climate As a simple example, consider the average daily maximum temperatures for two cities, one inland and one on the coast. The sample mean could serve as a good estimator of the population mean. Another strength of R is static graphics, which can produce publication-quality graphs, including mathematical symbols. This quantity is known as the standard deviation. In such cases the sample standard deviation should be used. Variation is 1 if and only if cases are evenly divided across all categories. A skewed distribution, on the other hand, is a distribution with extreme values on one side or the other that force the median away from the mean in one direction or the other. The Mean The mean is what people typically refer to as "the average". As an example of why the mean might not be the best measure of central tendency for a skewed distribution, consider the following passage from Charles Wheelan's Naked Statistics: Stripping the Dread from the Data : "The mean, or average, turns out to have some problems, namely, that it is prone to distortion by "outliers," which are observations that lie farther from the center. A statistic is biased if it is calculated in such a way that is systematically different from the population parameter of interest. Skewed Distributions A symmetrical distribution is a distribution where the mean, median and mode are the same.

It is the simplest measure of qualitative variation. The standard deviation is the most robust measure of variability since it takes into account a measure of how every value in the dataset varies from the mean.

That smaller dimension is the number of degrees of freedom for error.

## Measures of variability statistics slideshare

The range is a measure of the total spread of values in a quantitative dataset. The Range The range is the difference between the largest and smallest values in a set of values. Descriptive statistics, however, lacks the ability to identify the cause behind the phenomenon, correlate associate data, account for randomness, or provide statistical calculations that can lead to hypothesis or theories of populations studied. Effects of Changing Scale: In this graph, the earnings scale is greater. One piece of information cannot vary because its value is fully determined by the parameter in this case the mean and the other scores. However, if one of the values in column A was found to be incorrect and adjusted, the cell range method would automatically update the calculation of the standard deviation whereas the longer format will require manual adjustment of the command. 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. Further information about using Excel to perform calculations can be found here. Imagine starting with a small number of data points and then fixing a relatively large number of parameters as we compute some statistic. Calculating the Inter-quartile range using Excel The method Excel uses to calculate quartiles is not commonly used and tends to produce unusual results particularly when the dataset contains only a few values.

Repeat with numbers above the median of the full set: 19, 21,

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