Median

The Arithmetic Median calculator computes the median  for a set of comma separated number values (`X_i`). 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:

• `X_i`: 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 (`X_i`) 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+188)/2 =  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 

• To compute the observation statistics for a set including min, max, mean, mid-point, median, count, population and sample variance and standard deviation, CLICK HERE.
• To sort a list of numeric values, CLICK HERE.
• To create a random subset of the a list of numeric values, CLICK HERE.
• Click here to see hundreds of statistics topics on vCalc
• Click here to apply some of the simplest statistics
• Start here with the basics of elementary statistics
• Click here to get a simplified view of mathematics
• Click here to understand the basic concept of Quantization
• Click here to read about frequency distributions
• Begin with the math of measuring central tendencies
• Click here to see basic psychology statistics
• Click here to see the category of Statistics in vCalc content
• Peruse the category of Engineering Probability and Statistics
• Try the Mean calculation
• Try the Median calculation
• Try the Mode calculation
• Try the Range calculation
• Try the Min calculation
• Try the Max calculation