Mode

In a set of numbers, the mode is the value with the highest frequency.  In the set of numbers below, the modal value is 3.

Values: 2,3,3,4       Mode=3

The value of the mode is that it reflects the common experience, its the value that occurs most often.  When people are are asked to give an average value, say, for the time it takes them to get to work, they are most likely to give the time it usually takes them rather than the result of a calculation based on recorded journey times.

The mode is a good summary statistic for data sets which are skewed.  The bar chart shows the distribution of wind speed over the period of a year.  The distribution of wind speed is almost always left skewed meaning that the mode is less than the mean.

The bar with the greatest height indicates the mode.

The advantage of the mode over the mean is that it is less sensitive the presence of anomalous values in the data:

Related topics

The Mean
The Median
Estimation of the mode by successive bisection

Calculation

Unlike the the calculation of the mean and median, there is no single accepted method for calculating the mode of a sample of values from a continuous distribution.  The simplest way of calculating the mode is based on a histogram:

Step 1

Divide the range into an appropriate number of intervals.

Step 2

Determine the number of values which fall into each interval.

Step 3

Identify the interval with greatest number of values, then estimate the mode by taking the mean of the lower and upper values of the interval.

An example is shown in graphic form below:

This approach is sensitive to the size of the interval chosen.  With large datasets it may be possible to increase the precision of the estimate by using small interval sizes, however, a small one may make it difficult to get a reliable result.

Spreadsheets

MS Excel and Google Docs both provide functions which can be used to estimate the mode.  The Mode function works with discrete values, returning the value with the highest frequency in the dataset, in the example below, the function returns 2:

=mode(1,2,2,3)

The example below contains decimal values as the argument and returns 2.5

=mode(1.5,2.5,2.5,3.5)

If all the values are unique, as in the example below and no mode can be identified, the function returns #NA

=mode(1,2,3)

The frequency function can be used with continuous variables.  In the Office XP version of Excel, the frequency function it is an array function and can not simply be cut and pasted.  The frequency function takes two arguments, the first is the range of values to analyse and the second is described as a bin array, it is a column of ascending numbers which represent the upper bound of an interval.  The frequency function "bins" the values such that it provides the count of the number of values which are less than or equal to the upper bound of the interval and greater than the upper bound of the preceeding interval.  The syntax is:

=frequency(values,bin array)

The image below shows the function being entered:

After it has been entered as an array function, the result is:

In this example, the modal interval would be identified as:

2.0 < Modal Interval <= 3.0

The values in the count column can be used to create bar or column charts or calculate relative frequency.