Calculate the arithmetic mean, median, mode, weighted average, standard deviation, and range instantly in your browser with full step-by-step mathematical explanations.
| Sum / Total (Σx): | 0 | Range (Max − Min): | 0 |
| Minimum Value: | 0 | Maximum Value: | 0 |
| Sample Std Dev (s): | 0 | Population Std Dev (σ): | 0 |
| Geometric Mean: | N/A | Harmonic Mean: | N/A |
Enter each value along with its respective weight (e.g. course grade + credits, or score + weight percentage).
| Item # | Value (x) | Weight (w) | Action |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 |
In mathematics and statistics, an average (or central tendency) summarizes an entire data set with a single representative number. Depending on the distribution of your data and whether individual data points carry different importance, different measures of central tendency are appropriate.
| Measure | Formula / Definition | Best Use Case |
|---|---|---|
| Arithmetic Mean | Sum of all values ÷ Total count (N) |
Evenly distributed datasets with no extreme outliers (e.g. test grades, height measurements). |
| Median | The middle value in an ordered set |
Skewed datasets with large outliers (e.g. real estate house prices, household income). |
| Mode | The most frequently appearing number |
Categorical data, survey popular choices, retail inventory sizing (e.g. shoe sizes). |
| Weighted Average | Σ(w × x) ÷ Σw |
College GPA calculations, financial investment portfolio returns, course module grades. |
Suppose a student has three assignments with different weights in their syllabus:
Calculation: (90 × 0.20) + (80 × 0.30) + (95 × 0.50) = 18 + 24 + 47.5 = 89.5%. The student's weighted average grade is 89.5.
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