What are Mean, Median, and Mode?
In statistics, the mean, median, and mode are measures of central tendency. They describe the center of a data set using three different methods.
Depending on the nature of your data (e.g., presence of outliers, categorical vs. numerical), one measure may be more representative than the others.
Mean: The arithmetic average. Calculated by adding all numbers and dividing by the count.
Median: The middle value when the data is ordered from least to greatest.
Mode: The number that appears most frequently in the data set.
How to Calculate Them Manually
Understanding the formulas helps you interpret the results provided by this calculator.
- Calculating the Mean: Sum all the values in your set. Let's say you have test scores of 80, 90, and 100.
The sum is 270. Since there are 3 scores, you divide 270 by 3. The Mean is 90.
- Calculating the Median: Sort your data. If you have 5 numbers, the median is the 3rd number.
If you have an even set of numbers (e.g., 1, 3, 5, 7), the median is the average of the two middle numbers: (3+5)/2 = 4.
- Calculating the Mode: Look for the number that repeats the most.
In the set {2, 2, 5, 7}, the mode is 2. Some sets have multiple modes (bimodal), and some have no mode if all numbers are unique.
When to Use Mean vs. Median
A common question in data analysis is which statistic to report. The choice depends heavily on "outliers"—values that are significantly higher or lower than the rest of the data.
For example, consider the annual salaries of 5 people in a small company: $40k, $45k, $50k, $55k, and $1M (the CEO).
- The Mean salary is $238k. This is misleading because no one actually earns close to that amount except the CEO.
- The Median salary is $50k. This accurately reflects what a typical employee earns.
Therefore, use the Median when your data is skewed or has outliers. Use the Mean when the data is normally distributed (a classic bell curve) without extreme values.
Frequently Asked Questions
What if there is no mode?
If no number in the data set repeats (e.g., 1, 2, 3, 4, 5), then there is no mode. In this calculator, the result will display "No Mode".
Can I use negative numbers or decimals?
Yes, absolutely. This calculator supports positive integers, negative integers, and decimals (e.g., -5, 3.14, 100). The calculation logic handles all standard real numbers.
What is the Range used for?
The Range is a measure of dispersion. It tells you how spread out the data is. A small range indicates the data points are close to each other, while a large range indicates high variability.