Descriptive Statistics Calculator
Free online descriptive statistics calculator. Compute mean, median, mode, standard deviation, variance, quartiles, skewness, and more from your data.
Accepts numbers separated by commas, spaces, tabs, or new lines
How to Use the Descriptive Statistics Calculator
Enter your data values separated by commas, spaces, or new lines. The calculator computes all major descriptive statistics instantly.
Statistics Calculated
Measures of Central Tendency
| Statistic | Description |
|---|---|
| Mean | Arithmetic average of all values |
| Median | Middle value when data is sorted |
| Mode | Most frequently occurring value(s) |
Measures of Dispersion
| Statistic | Description |
|---|---|
| Standard Deviation | Average distance from the mean |
| Variance | Square of standard deviation |
| Range | Maximum minus minimum |
| IQR | Interquartile range (Q3 - Q1) |
| CV | Coefficient of variation (relative spread) |
Distribution Shape
| Statistic | Description |
|---|---|
| Skewness | Measure of asymmetry |
| Kurtosis | Measure of tail heaviness |
Understanding the Results
Mean vs. Median
- If mean ≈ median: Data is approximately symmetric
- If mean > median: Data is right-skewed (pulled by high values)
- If mean < median: Data is left-skewed (pulled by low values)
Standard Deviation
- Low SD: Data points cluster closely around the mean
- High SD: Data points spread widely from the mean
The 68-95-99.7 rule for normal distributions:
- ~68% of data falls within 1 SD of the mean
- ~95% of data falls within 2 SDs of the mean
- ~99.7% of data falls within 3 SDs of the mean
Skewness Interpretation
| Value | Interpretation |
|---|---|
| ≈ 0 | Symmetric |
| > 0 | Right-skewed (positive skew) |
| < 0 | Left-skewed (negative skew) |
| |skew| < 0.5 | Approximately symmetric |
| |skew| > 1 | Highly skewed |
Kurtosis Interpretation
| Value | Interpretation |
|---|---|
| ≈ 0 | Normal (mesokurtic) |
| > 0 | Heavy tails (leptokurtic) |
| < 0 | Light tails (platykurtic) |
Population vs. Sample Statistics
This calculator provides both:
| Type | Standard Deviation | Variance | When to Use |
|---|---|---|---|
| Population | σ = √(Σ(x-μ)²/N) | σ² | When data is the entire population |
| Sample | s = √(Σ(x-x̄)²/(n-1)) | s² | When data is a sample (most common) |
The sample statistics use (n-1) in the denominator (Bessel’s correction) to provide an unbiased estimate.
The Five-Number Summary
The five-number summary provides a quick overview of data distribution:
- Minimum: Smallest value
- Q1 (25th percentile): 25% of data falls below
- Median (50th percentile): Middle value
- Q3 (75th percentile): 75% of data falls below
- Maximum: Largest value
This summary is the basis for box plots (box-and-whisker diagrams).
Detecting Outliers
Using the IQR method:
- Lower fence: Q1 - 1.5 × IQR
- Upper fence: Q3 + 1.5 × IQR
Values beyond these fences are potential outliers.
Example Interpretation
For the sample data: 12, 15, 18, 22, 25, 28, 30, 35, 38, 42, 45, 48, 52, 55, 60
| Statistic | Value | Interpretation |
|---|---|---|
| Mean | 35.0 | Center of data |
| Median | 35.0 | Mean ≈ Median suggests symmetry |
| Std Dev | 15.2 | Moderate spread |
| Skewness | 0.0 | Symmetric distribution |
| IQR | 27 | Middle 50% spans 27 units |
When to Use Different Measures
Use Mean when:
- Data is symmetric
- No extreme outliers
- Interval or ratio scale
Use Median when:
- Data is skewed
- Outliers are present
- Ordinal scale acceptable
Use Mode when:
- Finding most common category
- Nominal scale data
- Describing typical case
Related Resources
- Measures of Central Tendency - Mean, median, mode
- Standard Deviation - Understanding spread
- Data Visualization - Graphing your data
- Histogram Generator - Visualize distributions
- Standard Deviation Calculator - Quick SD calculation
Frequently Asked Questions
What are descriptive statistics?
Descriptive statistics summarize and describe the main features of a dataset. They include measures of central tendency (mean, median, mode), measures of spread (standard deviation, variance, range, IQR), and shape measures (skewness, kurtosis).
What is the difference between mean, median, and mode?
Mean is the arithmetic average (sum divided by count). Median is the middle value when data is sorted. Mode is the most frequently occurring value. Use median when data has outliers or is skewed; use mean for symmetric data.
What does standard deviation tell you?
Standard deviation measures how spread out the data is from the mean. Low SD means data clusters near the mean; high SD means data is spread widely. About 68% of normally distributed data falls within 1 SD of the mean.
What is the five-number summary?
The five-number summary consists of: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. It provides a quick overview of data distribution and is used to create box plots.
How do I detect outliers in my data?
Use the IQR method: outliers are values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR. Alternatively, values more than 3 standard deviations from the mean are often considered outliers.
Should I use population or sample statistics?
Use sample statistics (n-1 denominator) when your data is a subset of a larger population—this is almost always the case. Use population statistics only when you have data for the entire population.
Want to learn the theory?
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