Introduction

When analyzing data, it's important to understand the different ways we can describe the "center" or "typical value" of a dataset. The three most common measures of central tendency are mean, median, and mode. Each provides unique insights and is useful in different situations.

Mean

The mean, often called the average, is calculated by adding up all the values in a dataset and dividing by the number of values. It is sensitive to extreme values (outliers), which can skew the result.

Formula:
Mean = (Sum of all values) / (Number of values)

Example:
For the dataset [2, 3, 5, 7, 13],
Mean = (2 + 3 + 5 + 7 + 13) / 5 = 30 / 5 = 6

Median

The median is the middle value when the data is arranged in order. If there is an even number of values, the median is the average of the two middle numbers. The median is less affected by outliers and skewed data.

Example:
For the dataset [2, 3, 5, 7, 13], the median is 5 (the third value in the ordered list).
For [2, 3, 5, 7], the median is (3 + 5) / 2 = 4.

Mode

The mode is the value that appears most frequently in a dataset. There can be more than one mode if multiple values have the same highest frequency, or no mode if all values are unique.

Example:
For the dataset [2, 3, 3, 5, 7], the mode is 3.
For [2, 3, 5, 7], there is no mode.

Conclusion

Mean, median, and mode each offer a different perspective on the "center" of a dataset. The mean is useful for data without extreme outliers, the median is best when the data is skewed or contains outliers, and the mode highlights the most common value. Understanding when and how to use each measure helps you interpret data more accurately and make better decisions based on your analysis.