What Is the X-Bar in Statistics?

Peter Scholey/Photographer’s Choice/Getty Images

In statistics, an x-bar indicates the average or mean value of the random variable “x.” A bar over any capital letter indicates the mean value of a random variable.

The mean value of “x” is obtained from repeated observations of the value of “x.” To calculate x-bar, observe the value of “x” n times. Then, add all of the observed values of “x” and divide the sum by n. The resulting quantity is the mean value of “x,” the x-bar. Because “x” is a random variable, x-bar is not the same number if it is measured repeatedly.

The x-bar should not be confused with the other average quantities, the median and the mode. The median indicates the middle of the observed values of “x.” Calculate the median by arranging the observed values in numerical order and finding the value in the middle or, if there is an even number of values, the mean of the two middle values. The mode is the most commonly observed value of “x.” The value with the highest number of observations, if there is such a value, is the mode. When there is no value that occurs more often than other values, the data set has no mode.