Comparing Mean, Median, and Mode
Difference between median, mode and mean is presented in tabular form:
| Statistic | Definition | Formula | Usefulness |
|---|---|---|---|
| Mean | The average taken of given observations. Add up all the numbers and divide by the total number of terms. | [Tex]\text{Mean} (\bar{x}) = \frac{\sum x}{N}[/Tex] | Widely preferred for normally distributed data. |
| Median | The middle number in a given set of observations. Place all the numbers in ascending or descending order. Take out the middle number, which is the median. | If n is odd: [Tex]\text{Median} = \left(\frac{n + 1}{2}\right)[/Tex]th observation If n is even: [Tex]\text{Median} = \frac{n}{2}\text{th observation} + \frac{n}{2}+1\text{th observation} /2[/Tex] | Best representative for skewed data. |
| Mode | The most frequently occurred number in a given set of observations. The mode is derived when a number has the highest frequency in a series. The mode can be one or more than one. It is possible to have no mode at all. | The mode is the most frequently occurring observation or value. | Preferred for nominal distribution of data. |
Average Value and Calculation
Understanding averages is a fundamental aspect of quantitative analysis across various fields, from finance to academia, from sports to business. Whether it’s determining the average income of a population or the average score of a student, the concept of average value serves as a crucial tool for summarizing data and drawing meaningful insights. In this article, we delve into the essence of average value, its significance, and the methods to calculate it.
Table of Content
- What is Average Value?
- Types of Averages
- Arithmetic Mean
- Median
- Mode
- Comparing Mean, Median, and Mode
- Solved Examples on Average Value
- Practice Questions on Average Value