Descriptive Statistics Calculator

Get a complete summary of your dataset in seconds. Calculate mean, median, mode, range, standard deviation, quartiles, and more to understand the basic features of your data.

Descriptive Statistics Calculator

Calculate comprehensive descriptive statistics for your dataset

Data Values

Count (n)

Sum

782.00

Mean

39.10

Median

36.50

Mode

None

Min

12.00

Max

80.00

Range

68.00

Variability

Variance (sample)

370.6211

Std Dev (sample)

19.2515

Std Dev (population)

18.7641

Coefficient of Variation

49.24%

Standard Error

4.3048

Sum of Squares

7041.8000

Distribution

Skewness

0.5249

Positively skewed

Kurtosis (excess)

-0.6655

Platykurtic (light tails)

Percentiles & Quartiles

10th

18.00

25th (Q1)

25.00

50th (Median)

36.50

75th (Q3)

55.00

90th

70.00

IQR (Q3 - Q1): 30.00

About Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. They include measures of central tendency (mean, median, mode), variability (variance, standard deviation), and distribution shape (skewness, kurtosis).

Skewness: Measures asymmetry. Positive = right tail, Negative = left tail.
Kurtosis: Measures tail heaviness. Positive = heavy tails, Negative = light tails.

How the Descriptive Statistics Calculator Works

Enter your dataset as numbers separated by commas, spaces, or newlines. The calculator accepts integers, decimals, positive and negative values. Large datasets process quickly with comprehensive results.

The tool calculates measures of central tendency (mean, median, mode), measures of spread (range, variance, standard deviation, IQR), and distribution shape (skewness, kurtosis). It also computes quartiles, percentiles, and the five-number summary.

Results display in an organized table with clear labels. A histogram shows the distribution shape. Box plot visualization highlights the spread and any outliers. All statistics update instantly as you modify your data.

When You'd Actually Use This

Exploratory data analysis

Get your first look at a new dataset. Understand the basic characteristics before running complex analyses. Identify data quality issues early.

Report generation

Create summary statistics for stakeholder reports. Provide mean, median, and spread measures to give a complete picture of your data.

Quality control dashboards

Monitor process metrics over time. Track mean and standard deviation of key measurements to ensure consistent product quality.

Academic research

Report sample characteristics in research papers. Descriptive statistics are required in the methods or results section of most studies.

Business intelligence

Summarize sales, customer, or operational data. Understand typical values and variability to make informed business decisions.

Data validation

Check if data looks reasonable. Unexpected min/max values or unusual skewness can reveal data collection or entry problems.

What to Know Before Using

Mean is sensitive to outliers.Extreme values pull the mean toward them. Median is more robust. Report both when data is skewed or has outliers.

Standard deviation uses same units as data.Variance is in squared units, harder to interpret. SD is in original units, making it easier to understand spread in context.

Skewness indicates asymmetry.Positive skew: long right tail (like income). Negative skew: long left tail. Zero skew: symmetric distribution.

IQR shows middle 50% spread.Interquartile range (Q3 - Q1) is resistant to outliers. Better than range for describing typical spread in skewed data.

Pro tip: Always visualize your data alongside descriptive statistics. Anscombe's quartet proves datasets can have identical statistics but completely different patterns. Graphs reveal what numbers hide.

Common Questions

When should I use median instead of mean?

Use median for skewed data or data with outliers. Income, home prices, and reaction times are often skewed. Mean is fine for symmetric distributions.

What's the difference between sample and population SD?

Sample SD divides by (n-1), population SD divides by n. Use sample SD when your data is a subset of a larger population you're studying.

What does kurtosis tell me?

Kurtosis measures tail heaviness. High kurtosis: more extreme values than normal. Low kurtosis: fewer extremes. Normal distribution has kurtosis of 3.

Can standard deviation be negative?

No. SD is always zero or positive. Zero SD means all values are identical. Larger SD means more spread in the data.

What's the coefficient of variation?

CV = (SD / mean) × 100%. It's relative variability as a percentage. Useful for comparing spread across datasets with different units or scales.

How do I interpret skewness values?

Between -0.5 and 0.5: approximately symmetric. -0.5 to -1 or 0.5 to 1: moderately skewed. Beyond ±1: highly skewed.

What's the five-number summary?

Minimum, Q1, median, Q3, maximum. These five values describe the distribution's center, spread, and range. Used to create box plots.

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