Arithmetic Mean Calculator – Sum ÷ Count

The arithmetic mean balances the data: deviations above and below it cancel exactly. For 7, 8, 9, 12 the sum is 36 over 4 values, so x̄ = 9. The deviations are −2, −1, 0 and +3, and they total 0 — a property the calculator demonstrates on every run because it confirms the computation. The mean reacts to every value, which makes it sensitive to outliers: swap 12 for 120 and the mean leaps from 9 to 36 while the median would stay 8. Weighted versions apply when values carry different importance: grades 70 (weight 2) and 90 (weight 3) average (70×2 + 90×3)/5 = 82, not 80. The output includes sum, count, mean, the deviation list and the squared deviations sum Σ(x−x̄)² = 14, ready to become variance 14/4 = 3.5.

1. 1

   Enter your data set

   Values separated by commas, spaces or newlines

2. 2

   Sum the values

   The total Σxᵢ is displayed first

3. 3

   Divide by the count

   x̄ = Σxᵢ/n to any precision you choose

4. 4

   Inspect deviations

   Each x − x̄ is listed and sums to zero — the built-in check

• 1

  Deviations from the mean always sum to zero — use it as a free check

• 2

  One extreme value can move the mean far: 7,8,9,120 averages 36

• 3

  Weighted mean divides Σwx by Σw, not by the count of values

• Dividing by the wrong count after blank cells or duplicates sneak in

• Averaging averages of unequal group sizes without reweighting

• Using the mean of ratios when the total-of-totals mean is required

• Reporting many decimals when the data itself is coarse