📊 Mean, Median & Mode Calculator – Mathematical Explanation
1. Mean (Arithmetic Average)
Definition:
Suppose we have a dataset consisting of
real numbers:
The arithmetic mean is defined as:
Example:
For the dataset
:
2. Median
Definition:
The median is the middle value of an ordered dataset (sorted in ascending order).
-
If
is odd:
-
If
is even:
Example:
-
Dataset
Median = 3
-
Dataset
: Median =
3. Mode
Definition:
The mode is the value (or values) that occurs most frequently in a dataset. Depending on the data:
-
It can have one mode (unimodal)
-
Multiple modes (bimodal or multimodal)
-
Or no mode if all values occur with the same frequency.
Example:
-
Dataset
: Mode = 4
-
Dataset
: Mode = 2 and 5 (bimodal)
4. Importance in Statistics
-
Mean: Represents the central tendency of the data but is sensitive to outliers.
-
Median: Provides a better measure of central tendency when the dataset contains extreme values.
-
Mode: Indicates the most common or popular value, useful in surveys, education, and social sciences.
Together, these three measures provide a solid foundation for statistical analysis and data interpretation.
5. How to Use the Calculator
-
Enter your dataset (numbers separated by commas, spaces, or new lines).
-
Press Calculate to compute the results.
-
The tool will display:
-
Number of values (
)
-
Sum of values (
)
-
Mean (
)
-
Median
-
Mode(s)
-
Ordered dataset (ascending)
-
-
Copy results or download them as a CSV file.
The Mean, Median & Mode Calculator allows you to apply these mathematical formulas instantly and accurately, saving time compared to manual calculation. It is an excellent resource for students, teachers, and anyone studying statistics and mathematics.