The basic pillars of statistics - Mean, Mode and Median


Mean

The mean is a statistical measure that represents the average value of a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the number of values.

The mean can be calculated using the following equation:

\[ \text{{Mean}} = \frac{{x_1 + x_2 + \ldots + x_n}}{{n}} \]

Mode

The mode is a statistical measure that represents the most frequently occurring value in a dataset. It is often used to identify the central tendency or the peak of the distribution.

The mode can be calculated by finding the value with the highest frequency in the dataset.

\[ \text{{Mode}} = \text{{Value with highest frequency}} \]

Median

The median is a statistical measure that represents the central value of a dataset. It divides the dataset into two equal halves: one half with values greater than the median and the other half with values less than the median.

To calculate the median, the dataset must be arranged in ascending order. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.

\[ \text{{Median}} = \begin{cases} \text{Data}\left(\frac{n+1}{2}\right) & \text{if } n \text{ is odd} \\ \frac{\text{Data}\left(\frac{n}{2}\right) + \text{Data}\left(\frac{n}{2} + 1\right)}{2} & \text{if } n \text{ is even} \end{cases} \]

Take an Example

Let's consider a sample dataset: 2, 3, 4, 7, 5, 11, 5, 8, 9, 6, 1

The mean (average) of the data "2, 3, 4, 7, 5, 11, 5, 8, 9, 6, 1" is approximately 6.

The mode of the data is 5 since it appears twice, more frequently than any other number.

The median of the data is 5. When the data is arranged in ascending order, it is the middle value.

Siddharth Mittal

Siddharth is a Signal & Information Processing graduate with an undergraduate degree in Electrical & Electronics Engineering. He enjoys programming and has a passion for travel, photography, and writing.