3.10:
Median
Median is one of the measures of the center. It is generally referred to as the middle value when the data are arranged in increasing or decreasing order. The median is denoted as x tilde.
Consider sample data on the exam preparation time of college students. To find out the median value, first, arrange the data in decreasing order of preparation time. The number precisely at the center of the data is the median.
What if there are even numbers of data values? There is no single middle value that can divide the data into two equal halves. In such a case, identify the two middle numbers. Then, determine the mean of these two numbers to arrive at the median.
Unlike the mean, the median is a resistant measure of the center. The addition or removal of a few extreme values does not change the median by large amounts.
So, the median is a preferred measure of the center when the extreme values in a sample data set are unknown or not important.
3.10:
Median
Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured by arranging the data elements in an increasing or decreasing order. Since this middle value is not affected by the precise numerical values of the outliers or fluctuations, it is insensitive to them. Hence, in cases where a data set may have outliers or the extreme values are not known, the median is a better measure of the central tendency than the mean.
The median may be the exact middle value of a data set, if the number of elements it contains is odd. If it is even, the median is equal to the average of the two middle values, but is not equal to either of the two values.
Calculating the median requires sorting the data set and calculating the number of elements it contains. Hence, there is no simple algebraic formula. However, standard softwares can easily compute the median of a data set.