## Understanding Mean, Median, and Mode

When it comes to data analysis, mean, median, and mode are three of the most commonly used statistical measures. Each of these measures provides unique insights into the central tendency, distribution, and frequency of a set of data.

## Mean

The mean, also known as the average, is calculated by adding up all the values in a data set and dividing by the total number of values. For example, if you have a data set of [5, 10, 15, 20], the mean would be (5 + 10 + 15 + 20) / 4 = 12.5.

## Median

The median is the middle value in a data set when the values are arranged in ascending or descending order. If the number of values is even, the median is calculated by taking the average of the two middle values. For example, in the data set [5, 10, 15, 20, 25], the median would be 15.

## Mode

The mode is the value that appears most frequently in a data set. A data set can have one, multiple, or no mode. For example, in the data set [5, 10, 15, 10, 20], the mode would be 10.

## Example:

Consider the following data set: [1, 2, 3, 4, 5, 5, 6, 6, 6]. The mean is (1 + 2 + 3 + 4 + 5 + 5 + 6 + 6 + 6) / 9 = 4.33, the median is 5, and the mode is 6.

## Case Study:

In a survey conducted among 100 participants about their monthly income levels, the mean income was found to be $45,000, the median income was $40,000, and the mode income was $50,000. This indicates that while the average income is $45,000, the most common income level reported by participants is $50,000.

## Statistics:

- Mean: 67
- Median: 60
- Mode: 72

When analyzing data, it is essential to consider all three measures of central tendency to gain a comprehensive understanding of the distribution and characteristics of the data set.