Median

Another measure of central tendency is the median. This number is the middle value in a set of numbers that has been arranged lowest to highest. For example, find the median of this set: 2, 4 , 6, 9, 20,

Solution

The data set has already been arranged in order, lowest to highest: the lowest number is 2, the next one is 4, and so on. The median would therefore be the third number, which is 6. The median is a good central tendency measure in a set in which the data is skewed. A skewed data set is one in which one or more numbers is much larger or much smaller than the rest.  The median is calculated by arranging the numbers in rank order from smallest to largest, and labeling the number in the middle rank. If the data set has an even number of data points, the median is defined as the mean of the numbers in the middle two ranks. For example, the sets of numbers { 1, 3 , 5, 6, 20, 21} is already arranged in order from lowest to highest, and since there is an even number of data points in this set, the median is calculated by taking the mean of the two middle ranked numbers, in this case the 3rd and 4th numbers, which are 5 and 6.

Therefore, (5 + 6)รท 2 = 5.5

so x = 5.5