How to Calculate Range Statistics
Statistical measures help summarize a set of data. Calculating different types of range statistics enables you not only to measure the amount of variation, or spread, in your data, but also to calculate an average measure to describe the entire set. Range statistics have the advantage of being easy to calculate, but they must be carefully interpreted.
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Instructions
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At Home With the Range
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1
Enter your data onto a spreadsheet, such as Microsoft Excel, for analysis. This will be especially important if you have a large set of data. If you have a small set of only 10 observations or fewer, you can use a calculator.
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2
Array the data in your spreadsheet so that they are ordered from the lowest value to the highest. Many spreadsheet programs have a command that will allow you to do this easily. Range statistics are derived from the lowest and highest values in the data set.
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3
Identify the quartiles, measures that divide your ordered data into four quarters. The first quartile is the value at which 25 percent of the observations are smaller. The second quartile is the median value. The third quartile is the value at which 75 percent of the observations are smaller and 25 percent are larger. This step is especially helpful with large data sets but may not be necessary with a small set.
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4
Calculate the range, which will measure the amount of dispersion in the data. The range is the difference between the values of the largest and smallest observations in a set of data. For example, suppose we have a set of math test scores for a classroom of 25 students, in which the highest grade is 98 and the lowest is 50. Subtracting the lowest from the highest gives us a range for this example of 48.
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5
Compute the average of your largest and smallest observations to obtain the midrange. Like the mean (the arithmetic average), the median and the mode, the midrange is a measure of central tendency. For our example here, the average of 50 and 98 gives us a midrange value of 74.
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6
Using the quartile values identified in Step 3, subtract the value of the first quartile from the third to obtain the interquartile range. This measure considers the level of dispersion in the middle half of the data and thus is not distorted by extreme values at the high or low end.
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Tips & Warnings
Because they involve the largest and smallest values in a data set, the range and midrange can be distorted measures if an outlier (a value that is extremely high or low, relative to the values of the other observations) is present.
