Location Parameters

Author: Dr. Hannah Volk-Jesussek
Updated: October 17, 2025

What are Mean, Median and Mode?

In descriptive statistics, mean, median and mode are location parameters. They are also called measures of central tendency or measures of location. Based on data collected in a sample, the location parameters provide information about where the "center" of the distribution lies.

Measures of location can be used to summarize or describe a list of data with only one parameter. An example would be that the average duration of studies of sports students at the university XY is 11.1 semesters.

Together with the dispersion parameters, the location parameters therefore describe a distribution in the statistics. The most commonly used location parameters are the mean, the mode and the median. All these measures describe the center of distribution in different ways. Which location parameter is used depends on the level of measurement of the variable and the robustness to outliers.

Mean (Arithmetic Mean)

The mean value is appropriate for metric variables, i.e. if a metric scale of measurement is given. It indicates where the center of gravity of a distribution can be found. In everyday life it is also called the "average".

The mean value can be calculated by adding up all the values of a variable and then dividing the sum by the number of oberservations/values.

Calculate the Mean

A group of 5 statistics students was asked how many cups of coffee they drink per week. The result is 21, 25, 10, 8 and 11 cups. The average is thus 15.

Tip: You can easily calculate the mean value or the desired location parameter for your data here with numiqo in the statistics calculator.

Geometric Mean and Quadratic Mean

When talking about mean or average, mostly the arithmetic mean is meant, but there are also other types of mean values. Other mean values are, for example, the geometric mean and the quadratic mean also called Root Mean Square (RMS).

• Geometric mean: If there are n positive numbers, the geometric mean is the nth root of the product of the n values.
• Root Mean Square : The root mean square is obtained by dividing the sum of the squares by the number of values and taking the square root.

Median

If the measured values of a variable are ordered by size, the value in the middle is the median. The median is therefore the "middle value" of a distribution. It leads to a division of the series into two parts: one half is smaller and one is larger than the median.

Since for the calculation of the median the data are ordered, the variables must have ordinal or metric scale level.

For the median to be calculated, the scale level must be ordinal or higher. Ordinal scaling means that there is a ranking order between the values of a variable. This applies, for example, to school grades (ordinal) or salary (metric). However, it is not possible to create a ranking for a variable Place of birth and therefore the median cannot be calculated here.

If there is an odd number of characteristic values, then the median is a value that actually occurs.

If there is an even number of characteristic carriers (persons), the two middle characteristics are added together and their sum is divided by two.

Mean vs. Median

Compared to the mean, the median is much more robust to outliers. An outlier usually has little influence on the median, but it has a more or less large influence on the mean.

Mode (Modal Value)

The mode is the most common value. The mode is therefore the most frequent value in a distribution. It is therefore the value that is "typical" for a distribution.

The mode can be used for both metric and categorical (nominal or ordinal) variables.

Calculate the Mode

Example: In a sample of 70 managers from Berlin, 20 drive a Daimler, 25 a BMW, 10 a VW and 15 an Audi. The car brand BMW is the most common. Thus the mode is "BMW".

Therefore, the mode can easily be read in a frequency table, it is the most frequent observed value.

Attention: There can also be several mode values. If two or more points occur with the greatest frequency, then there are several mode values. In this case one speaks then of a bimodal or multimodal distribution.

Advantages and Disadvantages of the Mean, Median and Mode

If the distribution is symmetric, the mean and median are equal, and if the distribution is symmetric and unimodal, all three measures are equal. As a rule, however, the three measures have different values. Now, of course, the question is which of the measures of central tendency to use. Unfortunately, there is no clear rule for this, only a few decision aids.

Mean: The mean value is by far the most used. The disadvantages of the mean are that it is sensitive to outliers, the value does not have to exist in the data and for the interpretation to be meaningful, the data should have metric scale level.

Median: The great advantage of the median is that it is very robust to outliers and that the data only have to be scaled ordinally.

Mode: The mode is the value that occurs most frequently, which has the advantage that the value actually occurs. Furthermore, the mode can also be calculated for data that cannot be ordered and thus have a nominal scale level. The disadvantage is that the mode does not take into account the other existing data.

Example Location Parameter

With the Online Statistics Calculator numiqo you can calculate the mean, median and mode of your data.

That's how it works with numiqo: As an example, the score for a statistics exam can be used. To do this, copy the data into the Statistics Calculator, click on Descriptive Statistics and select the variable "Score".

The result then looks like this:

Calculate the mean:

The mean is calculated by dividing the sum of all values by the number of values.

Calculate the median:

Due to the even number of values, the median is obtained by adding the two middle values. The sum is then divided by two.