Measures of Central Tendency Mean The mean is the average of all numbers and is sometimes called the arithmetic mean. To calculate mean, add together all of the numbers in a set and then divide the sum by the total count of numbers. Median The statistical median is the middle number in a sequence of numbers. To find the median, organize each number in order by size; the number in the middle is the median. Mode The mode is the number that occurs most often within a set of numbers. ____________________________________________________________ Measures of Variability Range The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set. The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie. That’s why it’s preferred over many other measures of spread (i.e. the average or median) when reporting things like school performance or test scores. The interquartile range formula is the first quartile subtracted from the third quartile. Standard Deviation The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. Its symbol is σ (the lower case greek letter sigma). When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you have a relatively large standard deviation. Standard deviation is a measure of the dispersion of a set of data from its mean. If the data points are further from the mean, there is higher deviation within the data set. Standard deviation is calculated as the square root of variance by determining the variation between each data point relative to the mean.