The measures of center summarize a data set by finding its center or typical value. The mean, median, and mode are measures of center.
Mean: The sum of the data values divided by the number of values in the data set.
Median: The middle value when the data values are in numerical order. If the data set has an even number of values, the median is the mean of the two middle values.
Mode: The most common value or values in the data set.These measures allow us to draw important conclusions about our data set.
Measures of Variation
Although the measures of center give us a typical value in our data set, they do not tell us the full story of our data. Here is where the measures of variation come in handy. These measures represent the distribution of the data, or how much the data values vary from the center. Some commonly used measures of variation are range, interquartile range, and standard deviation.
Range: The difference between the maximum and minimum value of a data set.
Interquartile Range: The difference between the third and first quartiles of a data set. The first quartile Q_1 is the median of the lower half of the data and the third quartile Q_3 is the median of the upper half of the data.
Variance: The average of the distance of values from the mean squared.
These are often used together with a measure of center, to give an idea both of what a typical value is and how much the data can be expected to deviate from it.
