Calculator Suite
Descriptive Statistics Calculator
Descriptive AnalysisCalculate comprehensive statistical measures including mean, median, mode, standard deviation, and analyze data distributions with interactive visualizations.
Educational Resources
What they tell us:
- • Mean: Average value
- • Median: Middle value (50th percentile)
- • Mode: Most frequent value
- • Std Dev: Measure of spread
- • Skewness: Distribution symmetry
- • Kurtosis: Tail heaviness
Interpreting Skewness:
- • 0: Perfectly symmetric
- • >0: Right-skewed (long right tail)
- • <0: Left-skewed (long left tail)
- • ±0.5: Moderately skewed
- • ±1: Highly skewed
For Reliable Analysis:
- • Minimum 3 data points (preferably 10+)
- • Quantitative (numeric) data
- • Independent observations
- • Check for data entry errors
- • Consider outlier impact
When to Use Each Measure:
- • Symmetric data: Use mean
- • Skewed data: Use median
- • With outliers: Use IQR over std dev
- • Normal distribution: All measures valid
Descriptive statistics summarize your data with a few key numbers: The mean (average),median (middle value), mode (most common), and standard deviation (spread). These metrics tell you the center, shape, and variability of your dataset at a glance—essential before any advanced analysis.
Enter Your Data
Type numbers separated by commas, spaces, or newlines. Or paste from Excel/CSV.
Adjust Settings (Optional)
Set confidence level, histogram bins, and decimal precision as needed.
View Results
See mean, median, mode, standard deviation, quartiles, skewness, and more—instantly calculated.
Analyze Charts
Explore histogram, box plot, and frequency charts to visualize your data distribution.
📊 Example: Class Test Scores
Data: 72, 78, 81, 85, 87, 88, 92, 95
Mean
84.75
Median
86
Std Dev
7.41
Range
23
What This Calculator Assumes:
- • Data is quantitative (numeric values)
- • Observations are independent
- • Sample is representative of the population
- • No significant data entry errors
When to Use Caution:
- • Mean is sensitive to outliers—use median for skewed data
- • Small samples (n < 30) may not be representative
- • Categorical data requires different methods
- • Check for multimodal distributions
What is the difference between sample and population standard deviation?
Sample standard deviation divides by (n-1) to correct for bias when estimating from a sample. Population standard deviation divides by n when you have the complete dataset.
When should I use median instead of mean?
Use median when your data is skewed or has outliers. For example, income data is often right-skewed (a few high earners pull the mean up), so median income is more representative.
What does skewness tell me?
Skewness measures asymmetry. Positive skewness means a long right tail (mean > median). Negative skewness means a long left tail. Near zero indicates symmetry.
How do I interpret the confidence interval?
A 95% confidence interval means: if we repeated the sampling many times, 95% of the intervals would contain the true population mean.
What is IQR and why use it?
Interquartile Range (IQR) = Q3 - Q1. It measures spread of the middle 50% of data and is robust to outliers, unlike standard deviation.