 Measures of Spread

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An important concept in statistics is measures of spread or variation. A basic numerical description of a data set requires both measures of central tendency and spread. For example, say that you know that the average, or mean, income in a certain area is \$30,000. Taking this number alone, it could just as easily describe an area where incomes are spread out fairly evenly between \$25,000 and \$35,000, as an area where most of the incomes are \$10,000 and a few exceptionally hard-working and/or very lucky people have an income of \$1,000,000. This is where measures of spread come in.

Just as there are several measures (mean, median, mode) used to measure central tendency, there are also several measures of spread, including:

• Range, the difference between the lowest and highest values in a sample,
• Quartiles, representing values where 25%, 50%, or 75% of the data are below that value
• Variance, which describes how great a spread exists in the data
• Standard deviation, which describes the spread of data in relation to the mean.