When dealing with sparse data or data that is distributed towards the edges (U-Shaped sample), finding the Arithmetic Mean or Medium can provide wrong information about the data distribution. A way to calculate the average in such scenarios is to find where the data peaks exist. This method is called Mode.

The mathematical formula above with the sample examples can be found implemented in 5 different programming languages in our Github repository.

Examples

Example 1:

Consider the following simple set S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}. Using the formula above, as shown below in 3 simple steps we find the Mode for the sample S.

1. For each unique value in the set, count the number of occurances \begin{array}{c|c} \bold{Point} & \bold{Count} \\ \hline 1 & 1 \\ \hline 2 & 1 \\ \hline 3 & 1 \\ \hline 4 & 1 \\ \hline 5 & 1 \\ \hline 6 & 1 \\ \hline 7 & 1 \\ \hline 8 & 1 \\ \hline 9 & 1 \\ \hline \end{array}
2. Find the maximum occurrence maxima = 1
3. Return the set with the sample values with the maximum occurrence Mode = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}

Example 2

Workings:

1. For each unique value in the set, count the number of occurances \begin{array}{c|c} \bold{Point} & \bold{Count} \\ \hline 51 & 1 \\ \hline 97 & 1 \\ \hline 43 & 1 \\ \hline 20 & 1 \\ \hline 48 & 2 \\ \hline 96 & 1 \\ \hline 63 & 1 \\ \hline 10 & 1 \\ \hline 35 & 1 \\ \hline 16 & 1 \\ \hline 4 & 1 \\ \hline 42 & 1 \\ \hline 80 & 1 \\ \hline 18 & 1 \\ \hline 1 & 1 \\ \hline 67 & 1 \\ \hline 75 & 1 \\ \hline 46 & 1 \\ \hline 92 & 1 \\ \hline 38 & 1 \\ \hline 44 & 1 \\ \hline 87 & 1 \\ \hline 69 & 1 \\ \hline 54 & 1 \\ \hline 91 & 1 \\ \hline 6 & 1 \\ \hline 8 & 1 \\ \hline 60 & 1 \\ \hline 64 & 1 \\ \hline 53 & 1 \\ \hline 23 & 1 \\ \hline 86 & 1 \\ \hline \end{array}
2. Find the maximum occurrence maxima = 2
3. Return the set with the sample values with the maximum occurrence Mode = \{48\}