Mean vs Median: Difference and Comparison

Key Takeaways

1. The mean, often called the arithmetic average, is a fundamental concept in statistics and mathematics.
2. The median is another measure of central tendency often used alongside the mean.
3. The mean is calculated by summing all the values and dividing by the total count, while the median is determined by arranging values and selecting the middle one.

What is Mean?

The mean, often called the arithmetic average, is a fundamental concept in statistics and mathematics. It is a measure of central tendency that provides insight into the average value of a dataset. It is applied in fields such as economics, physics, and engineering.

The mean serves as a valuable tool for understanding the typical value of a dataset. However, extreme values, known as outliers, can influence it, which differ slightly from the rest of the data. It serves as a balance point that captures the collective magnitude of the data.

To calculate the mean, you sum up all the values in the dataset and divide them by the total number of values. It is a commonly used statistical measure that provides a representative discount that can be used to understand the value of a dataset. The mean is especially useful when dealing with numerical data, such as test scores, temperatures, or salaries.

What is a Median?

The median is another measure of central tendency that provides a different perspective on the value of a dataset. It is the middle value of a dataset arranged in ascending or descending order. If the dataset has an odd number of values, the median is the central value, and if the dataset has an even number of values, the median is the average of two middle values.

 It is a robust statistical measure with a unique dataset position. The median remains steadfast, offering insight into the central importance of the data without being swayed by outliers. This property makes the median valuable where you want to understand the typical value of a dataset.

One of the primary advantages of using the median is its ability to provide a more precise representation of the data’s distribution. It is also crucial when working with original data, which involves categories with a specific order or rank.

Difference Between Mean and Median

1. The mean is the average of a set of numbers, calculated by summing all values and dividing by the total count. At the same time, the median is the middle-value dataset when arranged in ascending or descending order.
2. The mean is sensitive to outliers, as a single extraordinarily high or low value can significantly affect its value. At the same time, the median is less sensitive to outliers since it only considers the middle value.
3. The mean is affected by the sample size, whereas the median remains unaffected by it.
4. The mean is commonly used in ratios or proportions calculations, while the median is used in income distribution or ranking data cases.
5. The mean reflects the central tendency of the data but can be skewed by extreme values, while the median represents the central value and is often used when data is skewed.

Comparison Between Mean and Median

Parameters	Mean	Median
Definition	The average of set numbers, calculated by summing all values and dividing by the total count	The middle-value dataset, when arranged in ascending or descending order
Sensitivity	Sensitive to outliers	Less sensitive
Sample size	Affected by it	Unaffected
Applications	Used in calculations involving ratios, proportions and to access overall trends	Used as income distribution or ranking data
Data distribution	Reflects the central tendency of the data	Represents the central value when data is skewed

References

1. http://siba-ese.unisalento.it/index.php/ejasa/article/view/11468
2. https://link.springer.com/article/10.1007/s10649-006-7099-8