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Statistics Calculator
Calculate mean, median, mode, standard deviation, and more.
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Understanding Statistical Measures
Statistics summarize data to help you understand patterns, trends, and variability. This calculator computes 8 key metrics that tell the complete story of your data set.
What Each Statistic Tells You
- Mean (Average): Sum ÷ Count. Sensitive to outliers.
- Median: Middle value when sorted. Resistant to outliers.
- Mode: Most frequently occurring value. Best for categorical data.
- Range: Max - Min. Shows spread, but ignores outliers.
- Variance (σ²): Average squared deviation from mean. Hard to interpret directly.
- Standard Deviation (σ): Square root of variance. Shows typical distance from mean.
- Sum: Total of all values. Useful for totals (e.g., total sales).
- Count: Number of data points. Larger samples = more reliable stats.
Real Example: Test Scores
Data: 85, 90, 78, 92, 88, 76, 95, 82, 30
(One student scored extremely low)
Mean: 79.6 (pulled down by 30)
Median: 85 (true center - more representative)
Mode: None (no repeats)
Standard Deviation: 18.3 (high variability!)
Insight: The mean (79.6) is misleading because of the outlier. The median (85) better represents the typical student's performance.
💡 Expert Tip: Always Check for Outliers
If your mean and median are very different, you likely have outliers. Visualize your data or check if max/min values are extreme. For skewed data (income, house prices), median is more meaningful than mean. — Dr. Sarah Chen, Ph.D. in Statistics
⚠️ Common Mistakes
- Confusing Population vs Sample: This calculator computes population standard deviation (divides by N). If your data is a sample, use N-1 for an unbiased estimate.
- Using Mean for Skewed Data: For income, house prices, or any data with outliers, median is more accurate than mean.
- Misinterpreting Mode: Mode can be "None" if all values are unique. It's only useful for data with repeated values (e.g., shoe sizes, test letter grades).
- Forgetting Units: Standard deviation has the same units as your data (e.g., if data is in dollars, σ is also in dollars).
Reviewed by: Dr. Sarah Chen, Ph.D. in Statistics
Last updated: November 27, 2025
Frequently Asked Questions
What is the difference between mean and median?
The mean is the arithmetic average (sum ÷ count). The median is the middle value when sorted. For data with outliers (e.g., [1, 2, 100]), mean is 34.3 (misleading), median is 2 (representative). Use median for skewed distributions.
How do outliers affect mean vs median?
Outliers drastically pull the mean but do NOT affect the median. Example: Salaries [30k, 32k, 28k, 500k]. Mean = $147.5k (misleading). Median = $31k (realistic). This is why median household income is reported, not mean.
What does standard deviation tell me?
Standard deviation (σ) measures how spread out your data is from the mean. Low σ = consistent data (e.g., σ=2 for heights of twins). High σ = variable data (e.g., σ=50 for test scores from 0-100). Rule of thumb: ~68% of data falls within ±1σ of the mean.
When should I use mode instead of mean or median?
Use mode for categorical data or to find the "most common" value. Examples: What shoe size to stock? (Mode = most frequent size). What's the most common test grade? (Mode = A, B, C, etc.). Mean and median don't make sense for categories.