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# Dispersion and Spread of Data

The dispersion and spread of data refers to measures in statistics which are used to define the deviation or scatter of a data set from the central value. Some of these measures, such as standard deviation and the interquartile range, are commonly seen marked on graphs to illustrate the variability which exists in the data set being presented. To describe data fully, knowing the extent of variability which is present is critical, and this cannot be achieved through the use of central tendency measures alone (1). Thus, using measures which evaluate the dispersion and spread of data is a common practice.

Using various measures of dispersion or spread in conjunction with measures of central tendency is very valuable in statistics. Using a measure of spread to assess the variability of a data set can provide insight as to whether a particular measure of central tendency will be useful in evaluating the data (2). Determining whether the variation of a data set is high or low can indicate whether or not the mean would be more appropriate than the median to use in finding the average value of a data set.

Essentially, the overall objective in using measures of dispersion and spread is to summarize the nature of data. Calculating the interquartile range, standard deviation or range, are some of the methods which can be implemented to estimate variability. Furthermore, utilizing different indicators of dispersion and spread can be an efficient method for making comparisons between data sets, and thus, educated conclusions regarding the importance of the results.

References:

1. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3198538/

## BrainMass Categories within Dispersion and Spread of Data

### Range

Solutions: 17

The range is a statistical measure which aims to calculate the spread between the minimum and maximum value in a data set.

### Standard Deviation

Solutions: 201

Standard deviation is a measure of absolute variation used to calculate the amount of divergence which exists from an expected value and is denoted by the Greek symbol for sigma.

### Coefficient of Variation

Solutions: 31

The coefficient of variation is computed by deriving the ratio between the standard deviation and the mean and thus, is known as a measure of relative variation.

### Percentile

Solutions: 49

Percentiles are often calculated for a set of data in statistics and are representative of different percentage ranges.

### Interquartile Range

Solutions: 9

In statistics, the interquartile range refers to the overall difference between the higher quartile value of a data set and the accompanying lower quartile value.

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