Median Definition and Calculation

You can easily calculate median, percentiles, standard deviation, skewness, kurtosis, and other measures in Excel using the Descriptive Statistics Calculator.

Median definition

Like arithmetic average, geometric average, or mode, median is one of the measures of central tendency of a population, a sample, or a probability distribution. Median is the value which divides a data set in two halves – one with values lower than the median and the other with the higher values.

Median calculation

The word “calculation” might sound as an overstatement with median, as there is in fact nothing you need to calculate. You only need to find the value that divides the data set exactly in two halves (half of the observations is below and the other half is above the median).

How to Calculate Median of an Odd Number of values

Let’s say a fund recorded the following performance in the last 5 years:

What is the median of the annual performance during this five year period?

First we need to sort the values from lowest to highest – we have: -3%, 1%, 5%, 8%, 19%. When the number of values (years in our case) is odd, it is easy to find the middle observation. The median is 5%.

Calculating Median of an Even Number of Values

It is less simple when there is an even number of observations, because in this case there is not a single one which could be considered “middle”. Let’s add the sixth year to the example above – in year 6 the fund’s performance was +17%. What is the median now?

First, we sort the data: -3%, 1%, 5%, 8%, 17%, 19%. There are six values now. Because the number of values is even, there are in fact two of them in the middle: 5% and 8%. In this case the median equals the mean of the two middle values: 6.5%.

Calculating Median in Excel

In Excel, you can calculate median using the built-in MEDIAN function. In the Descriptive Statistics Calculator, median is calculated in cell D10.

Multiple observations as the median

Sometimes there are multiple identical values equal to the median. For example, the median of 1, 2, 3, 3, 7 equals 3. In this case there are two of the observations equal to the median. Technically, the definition of median dividing a data set in two halves is a bit blurred here.

Median is the second quartile

If you are familiar with quantiles (statistical measures describing data sets), you see that median is the same concept – median is the name for the 2-quantile. The median is also the same as the second quartile, or as the fifth decile, or the 50th percentile.

Why use median?

Median performs the same function as mean or mode – it gives us an idea about the overall level or central value of a data set. You might have noticed reports about median household income or median house prices in the media.

In comparison with arithmetic average, median has some strengths and weaknesses. It addresses some of the well-known disadvantages of the arithmetic average: it works better with skewed data sets and it is less sensitive to extreme values (which might result from errors in measurement). On the other hand, median is much less possible to be further processed and used in further calculations compared to the arithmetic average.

You can easily calculate median, percentiles, standard deviation, skewness, kurtosis, and other measures in Excel using the Descriptive Statistics Calculator.

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