When to Use Mean vs Median vs Mode
Mean, median, and mode answer different questions about your data. Picking the wrong one gives you a misleading summary. The mean (arithmetic average) works best when your data is roughly symmetric with no extreme outliers. The median is your go-to when outliers skew the picture. The mode tells you what shows up most often.
A quick example: five salaries of $35K, $40K, $42K, $45K, and $500K produce a mean of $132K, a median of $42K, and no mode. The mean is pulled up by one outlier and misrepresents the group. The median of $42K is the honest answer here.
Mean vs Median vs Mode Comparison
| Measure | Formula | Best For | Sensitive to Outliers? |
|---|---|---|---|
| Mean | ∑x ÷ n | Symmetric data, scientific measurement, test scores | Yes |
| Median | Middle value (sorted) | Skewed data, incomes, home prices, response times | No |
| Mode | Most frequent value | Categorical data, shoe sizes, survey responses | No |
| Weighted Mean | ∑(x·w) ÷ ∑w | Grades, portfolio returns, survey scaling | Yes |
Standard Deviation Explained
Standard deviation (SD) measures how spread out your numbers are from the mean. A small SD means values cluster tightly around the average. A large SD means they are scattered.
The formula: take each number, subtract the mean, square the result, average those squared differences (that's the variance), then take the square root. Our calculator uses population standard deviation (σ), dividing by n rather than n−1.
σ = √(∑(x−μ)² ÷ n)
Two datasets can have the same mean but very different spreads. Test scores of {78, 80, 82} have SD = 1.63. Scores of {40, 80, 120} have SD = 32.66. Same mean (80), completely different stories. SD tells you how consistent or volatile your data really is.
Interpreting Standard Deviation
| SD Range | Interpretation | Example |
|---|---|---|
| Low (< 10% of mean) | Tight clustering. Values are consistent and predictable. | Factory quality control, repeated lab measurements |
| Moderate (10–30% of mean) | Normal variation. Typical spread for most real-world data. | Class test scores, daily temperatures |
| High (30–50% of mean) | Wide spread. Significant variation that may warrant investigation. | Stock returns, city home prices |
| Very High (> 50% of mean) | Extreme scatter. Data may contain outliers or subgroups. | Income distribution, viral content views |
Weighted Average Use Cases
A weighted average assigns different importance to each value. Without weights, every number counts equally. With weights, you control how much each number influences the final result.
| Use Case | Values | Weights | Why Weighted? |
|---|---|---|---|
| Course grades | Exam, homework, project scores | Credit hours or category percentages | A 4-credit A should count more than a 1-credit A |
| Portfolio returns | Individual stock/fund returns | Dollar amount in each position | $50K in stocks matters more than $500 in crypto |
| Customer reviews | Star ratings (1–5) | Number of reviews at each rating | 500 five-star reviews should outweigh 3 one-star reviews |
| Employee performance | Scores across categories | Category importance | “Meeting deadlines” might matter more than “office decor” |
| Survey results | Response values | Sample sizes or demographic weights | Corrects for over/under-representation in the sample |
Weighted Average Formula
Weighted Mean = ∑(value × weight) ÷ ∑(weights)
Example: Test 1 scored 90 (weight 3), Test 2 scored 80 (weight 2), Test 3 scored 70 (weight 1). Weighted mean = (90×3 + 80×2 + 70×1) ÷ (3+2+1) = 500 ÷ 6 = 83.33. The simple average would be 80. The weighted average pulls closer to 90 because Test 1 has the highest weight.
Related Tools
Need to calculate percentage changes or find what percent one number is of another? Use our percentage calculator. For course-specific grade calculations with letter grades and credit hours, the GPA calculator handles semester and cumulative GPA on a 4.0 scale.