How to Calculate Statistics
Our statistics calculator computes mean, median, mode, range, variance, and standard deviation. Essential for data analysis, research, quality control, and understanding distributions.
Understanding Basic Statistics
Statistics summarize data sets. Measures of central tendency (mean, median, mode) show typical values. Measures of spread (range, variance, standard deviation) show how data is distributed around the center.
Statistics Formulas
Mean = sum/count. Median = middle value when sorted. Mode = most frequent. Variance = average of squared deviations from mean. Standard deviation = √variance.
Example:
Data: 2, 4, 4, 6, 8. Mean = 24/5 = 4.8. Median = 4. Mode = 4. Variance = [(2.8² + 0.8² + 0.8² + 1.2² + 3.2²)]/5 = 4.16. SD = 2.04.
Common Use Cases
Real-world applications for this calculator
Academic Research
Analyze experimental data and survey results.
Business Analytics
Understand sales patterns, customer behavior, and trends.
Quality Control
Monitor manufacturing processes and detect anomalies.
Tips
- Use median when data has outliers (like income data).
- Standard deviation has the same units as the original data.
- Variance = SD²; easier to calculate but harder to interpret.
- For normal distributions: ~68% within 1 SD, ~95% within 2 SD.
Frequently Asked Questions
What is the difference between mean and median?
Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. Median is better for skewed data as it's not affected by outliers.
How do I calculate standard deviation?
Find the mean. Subtract mean from each value and square it. Average those squared differences (variance). Take the square root. For samples, divide by n-1 instead of n.
What does standard deviation tell me?
SD measures how spread out data is from the mean. Low SD means data clusters near the mean. About 68% of data falls within 1 SD of mean in a normal distribution.
When should I use mode?
Mode is useful for categorical data or when you want the most common value. A data set can have no mode, one mode, or multiple modes (bimodal, multimodal).
What is the difference between population and sample statistics?
Population includes all members of a group; sample is a subset. Sample variance divides by n-1 (not n) to correct bias. This is called Bessel's correction.