What is the Mean?

The mean (arithmetic average) is the sum of all values divided by the number of values. It's the most widely used measure of center in statistics.

mean = (x₁ + x₂ + ... + xₙ) / n = Σxᵢ / n

Key Properties:

Central marker: Minimizes the sum of squared deviations (mathematically optimal).
Easily calculated: Simple sum and divide operation.
Sensitive to outliers: Extreme values pull the mean away from the center.
Always exists: Every numeric dataset has a mean (unlike mode or median which may not be unique).
Foundation for advanced stats: Basis for variance, standard deviation, regression, hypothesis testing.

When to use mean: Symmetric distributions without extreme outliers. Normal/bell-curve data, financial returns, test scores (when fairly distributed).

When NOT to use: Skewed distributions, data with extreme outliers. Example: median home price is better than mean (outliers inflate mean).

How to Calculate the Mean

1

Gather your data

List all values in your dataset. Example: 10, 20, 30, 40, 50

2

Count the values

Determine how many numbers you have. n = 5 in our example.

3

Sum all values

Add them up: 10 + 20 + 30 + 40 + 50 = 150

4

Divide sum by count

mean = 150 / 5 = 30. The average is 30.

Example Calculation

Dataset: 10, 20, 30, 40, 50 Step 1: Count values n = 5 Step 2: Sum all values Σx = 10 + 20 + 30 + 40 + 50 = 150 Step 3: Calculate mean mean = Σx / n = 150 / 5 = 30 Interpretation: The average value is 30. This is the center point around which all values balance.

Mean Calculator

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