What is statistics? – Mode

What is Mode – A Historical view
Karl Pearson was one of the most influential, famous and great statistician that existed. He founded the world first Statistical University department in London. He was honored multiple times from UK government. He also invented the Mode among other things (1895).

What is Mode – Theoretical definition
Mode or modal value is defined as the value or values that has or have the highest frequency inside an arithmetic series. By this definition, it can be suggested that the Mode can be more than one value, that is, multiple Modes or Modal values can exist. Also, there are cases that no Mode or Modal value exists in a dataset: all numbers appear only once, without repeating themselves. When two Modes exist, the dataset can be called a Bimodal dataset. If multiple modes exist, then it can be called a Multimodal dataset.

Statistical definition of Mode value
A specific statistical formula for calculation of Mode/s does not exist.

A statistical example for Mode value / Modal value
Let’s say that you have a dataset with 10 values that corresponds to these ages: 23, 45, 30, 34, 34, 23, 43, 23,  23, 34. The value that appears more often is the age of 23 which appears four (4) times. If we had a different dataset, such as this one: 1, 1, 1, 1, 1, 1, then, the Mode value will be the “1” which appears 6 times. Now, another dataset includes these values: 1, 3, 4, 6, 8, 10. Here, no Modal / Mode value exists because all the values have the same frequency (f=1). Finally, if this type of dataset was given to us: 2, 2, 3, 3, 8, 10, then, we can suggest that there are two Mode values / Modal values and these values are: 2 and 3 which both appear 2 times, or otherwise, its frequency is the highest ones between the frequency that other numbers/values have.

In Summary:
a) 23, 45, 30, 34, 34, 23, 43, 23, 23, 34, Mode=23
b) 1, 1, 1, 1, 1, 1, Mode=1
c) 1, 3, 4, 6, 8, 10, Mode=No one or All of them
d) 2, 2, 3, 3, 8, 10, Mode=2, 3

statistical Mode value example

The Statistical relation of Mean, Median, and Mode
It is interesting that when the values of Mean, Median, and Mode coincide in a specific dataset, then it can be concluded that this dataset is normally distributed. Statistically, it can be written as: Mn=Md=Mo. Note that the Mean, Median, and Mode are measurements of the Central Tendency. The concept of Normality will be discussed in another section.

Karl Pearson: SAS blog