How do I use the Descriptive Statistics Calculator?

Enter your data in the input fields, then click Calculate. The calculator will show you the results along with step-by-step explanations of how the calculation was performed.

Is the Descriptive Statistics Calculator free?

Yes, this descriptive statistics calculator is completely free to use with no registration required. Use it as many times as you need for homework, research, or data analysis.

Can I use this calculator on mobile?

Yes, the descriptive statistics calculator is fully responsive and works on smartphones, tablets, and desktop computers.

Descriptive Statistics Calculator - Free Online Calculator

Enter 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

Measures of Central Tendency - Mean, median, mode
Standard Deviation - Understanding spread
Data Visualization - Graphing your data
Histogram Generator - Visualize distributions