Median Measure of Central Tendency

Median (a measure of central tendency) is the middle-most value in the data set when all of the values (observations) in a data set are arranged either in ascending or descending order of their magnitude. Median is also considered as a measure of central tendency which divides the data set in two halves, where the first half contains 50% observations below the median value and 50% above the median value. If in a data set there are an odd number of observations (data points), the median value is the single-most middle value after sorting the data set.

Example: Consider the following data set 5, 9, 8, 4, 3, 1, 0, 8, 5, 3, 5, 6, 3.
To find the median of the given data set, the first sort it (either in ascending or descending order), that is
0, 1, 3, 3, 3, 4, 5, 5, 5, 6, 8, 8, 9. The middle-most value of the above data after sorting is 5, which is the median of the given data set.

When the number of observations in a data set is even then the median value is the average of two middle-most values in the sorted data.

Example: Consider the following data set, 5, 9, 8, 4, 3, 1, 0, 8, 5, 3, 5, 6, 3, 2.
To find the median first sort it and then locate the middle-most two values, that is,
0, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 8, 8, 9. The middle-most two values are 4 and 5. So the median will be the average of these two values, i.e. 4.5 in this case.

The median is less affected by extreme values in the data set, so the median is the preferred measure of central tendency when the data set is skewed or not symmetrical.

For large data set it is relatively very difficult to locate median value in sorted data. It will be helpful to use median value using formula. The formula for odd number of observations is
Median &=\frac{n+1}{2}th\\
Median &=\frac{n+1}{2}\\

The 7th value in sorted data is the median of the given data.

The median formula for even number of observation is
Median&=\frac{1}{2}(\frac{n}{2}th + (\frac{n}{2}+1)th)\\
&=\frac{1}{2}(\frac{14}{2}th + (\frac{14}{2}+1)th)\\
&=\frac{1}{2}(7th + 8th )\\
&=\frac{1}{2}(4 + 5)= 4.5

Note that median measure of central tendency, cannot be found for categorical data

Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

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