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Median

X(median)=value separating lower half of values from upper half of values
(x)Numeric observations.
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Statistics

The Arithmetic Median calculator computes the median  for a set of comma separated number values (Xi). The media indicates at what value the center of the set of values is.

NOTE: many vCalc equations are embedded throughout vCalc descriptive pages like this page.  Even though they may not stand out in the text, if you hover over the name of an equation it will likely be linked to an actual, pop-up executable equation. For example: Arithmetic Mode

Inputs

Enter the following:

  • Xi: This is the set of comma-separated numeric values (e.g. 4.78,-1.2,8,9.901 )

You can copy and paste in the list of comma-separated values.

The Math 

The  calculator returns the arithmetic median for the entered values. This median is the input value in (Xi) that is halfway up the list of the ordered data set.

Example

Let our data set when ordered be:  2.222, 8, 16, 16.5, 18.8, 22, 27.82, 36, 40

Since the number of values in our data set is N=9, which is odd, we just find the middle number: Mode=18.8.   There are as many lower values below 18.8 as there are higher values above 18.8 -- which makes 18.8 the Mode of our data set.

Let our data set when ordered be:  100, 108, 161.5, 169, 188, 222, 227.82, 360.  Here N=8 is even, so there is no value in the list that has half the value lower and half the values higher.  So, we average the middle two values, 169 and 188 to get the Mode=169+1882= 178.5

You can try these two data sets by copying and pasting the example data sets into the vCalc equation for Median.

See Also