Mean · Median · Mode · Range Calculator

1. Mean (Arithmetic Average)

• Definition: The sum of all values in the data set divided by the number of values.
• Formula:

Mean Formula: x̄ = Σx_i / n

where

x_i are the data values and ( n ) is the number of values.

How to calculate?

• Add up all the numbers.
• Divide the total by how many numbers there are.

Best for:

• Data without extreme outliers (it's sensitive to outliers).

Example:

Data set = 2, 3, 5, 7, 10

Mean = (2 + 3 + 5 + 7 + 10) / 5 = 27 / 5 = 5.4

2. Median (Middle Value)

Definition: The middle value when the data is arranged in ascending order.

How to calculate:

• Sort the data from smallest to largest.
• If there is an odd number of values → the median is the middle one.
• If there is an even number of values → the median is the average of the two middle values.

Best for: Data with outliers or skewed distributions (it's resistant to extremes).

Example 1 (Odd): Data set = 2, 3, 5, 7, 10

Sorted: 2, 3, 5, 7, 10 → Median = 5 (middle value)

Example 2 (Even): Data set = 2, 3, 5, 7, 10, 12

Sorted: 2, 3, 5, 7, 10, 12 → Median = (5 + 7) / 2 = 6

3. Mode (Most Frequent Value)

Definition: The value(s) that appear most often in the data set.

How to calculate:

• Count the frequency of each value and pick the one(s) with the highest count.
• Notes:
• A set can have no mode (all values appear equally often).
• One mode → unimodal.
• Two modes → bimodal.
• More than two → multimodal.

Best for: Categorical data or identifying the most common occurrence.

Example: Data set = 2, 3, 3, 5, 7, 7, 7, 10

Mode = 7 (appears 3 times)

4. Range (Measure of Spread)

Definition: The difference between the highest and lowest values in the data set.

Formula: Range = Maximum - Minimum

How to calculate: Subtract the smallest value from the largest value.

Best for: Giving a quick sense of the spread of the data (but very sensitive to outliers).

Example: Data set = 2, 3, 5, 7, 10

Range = 10 - 2 = 8