In research, it is helpful to be able to describe the characteristics of a data set. Do the observations in the data set cluster around one central value or are they spread out? Descriptive statistics measure these characteristics.

Measures of
Central Tendancy

Measures of
Variability

Mean
Median
Mode

Range
Standard Deviation

The mean, median and mode provide information about the number in the middle of a data set. The mean is the same as the average. It is usually the best indicator of the middle of the data set unless the data set contains a large number of high or low data points. In these cases, the median is a better measure of central tendency. Examples of data sets where the median is usually a better measure of central tendency include housing prices and family income. The median is the middle number in the data set. The mode is the number that occurs most frequently. The mean, median and mode are equal in a normal distribution. In a skewed distribution, the mean and median are not equal and the mean shifts to one side of the distribution.

The range and standard deviation show how far data points spread out from the middle of the data set. The range is simply the highest number minus the lowest number. The standard deviation is a measure of how far data points are spread out from the mean of the data set. The larger the range and standard deviation are, the more the data points are spread out.

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