Descriptive Statistics Calculator

The Descriptive Statistics Calculator provides comprehensive statistical analysis of quantitative data. Calculates measures of central tendency, dispersion, position and shape including mean, median, mode, standard deviation, variance, quartiles, percentiles, skewness and kurtosis. Essential tool for researchers, statisticians, students and analysts who need detailed statistical analysis with outlier detection, frequency distribution and confidence intervals for data-driven decision making.

Updated at: 06/14/2025

How the Descriptive Statistics Calculator Works

The Descriptive Statistics Calculator is an essential tool for analyzing quantitative data in detail. It provides key statistical measures such as mean, median, mode, standard deviation, variance, interquartile range, percentiles, skewness, and kurtosis. Ideal for researchers, students, and professionals seeking a deep understanding of their data distribution and behavior.

This calculator enables precise exploratory analysis, helps identify outliers, assesses data spread, and compares distribution shapes. It delivers a general summary, central and positional statistics, shape analysis, and a frequency distribution, all from a simple data input.

Measures of Central Tendency

These statistics describe the center or typical value of the data:

  • Arithmetic Mean: 5.5000

  • Median: 5.5000

  • Mode: No mode (all values occur once)

  • Geometric Mean: 4.5287

  • Harmonic Mean: 3.4142

These values help determine the central point of the data distribution.

Measures of Dispersion

They indicate how spread out the data is from the mean:

  • Range: 9.0000 (maximum - minimum)

  • Variance: 9.1667

  • Standard Deviation: 3.0277

  • Coefficient of Variation: 55.05%

  • Mean Absolute Deviation: 2.5000

  • Interquartile Range (IQR): 6.0000

These metrics reveal the variability in your data set.

Positional Measures

These values divide the data into segments and highlight distribution points:

Five-number summary:

  • Minimum: 1.0000

  • Q1 (1st Quartile): 2.0000

  • Median: 5.5000

  • Q3 (3rd Quartile): 8.0000

  • Maximum: 10.0000

Key Percentiles:

  • P5: 1.4500

  • P10: 1.9000

  • P25: 3.2500

  • P50: 5.5000

  • P75: 7.7500

  • P90: 9.1000

  • P95: 9.5500

  • P99: 9.9100

Percentiles and quartiles provide insight into the data's distribution and spread.

Shape Measures

These help analyze symmetry and tail concentration:

  • Skewness: -0.0000 → Symmetrical distribution

  • Kurtosis: -1.5616 → Platykurtic distribution (flatter than normal)

Shape measures help detect biases or heavy/light tails in the distribution.

Additional Useful Statistics

  • Sum of all values: 55.0000

  • Sum of squares: 385.0000

  • Standard Error of the Mean: 0.9574

  • 95% Confidence Interval: [3.6234, 7.3766]

These figures help assess estimate accuracy and the precision of the mean.

Frequency Distribution

Value Frequency Percentage
1 1 10.00%
2 1 10.00%
3 1 10.00%
4 1 10.00%
5 1 10.00%
6 1 10.00%
7 1 10.00%
8 1 10.00%
9 1 10.00%
10 1 10.00%

This table displays how often each value appears and its relative percentage.

What Type of Data Can You Use?

The calculator works with two types of datasets:

  • Sample: a portion of a larger population

  • Population: the complete set of elements under study

In this example, a sample of 10 values was used:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Indicating the correct data type ensures accurate variance and error calculations.

What Does Negative Kurtosis Indicate?

A negative kurtosis value indicates a platykurtic distribution, which is flatter than a normal distribution. This means the data is more spread out and has lighter tails.

What Does Zero Skewness Mean?

A skewness of -0.0000 suggests a perfectly symmetrical distribution, with balanced data around the mean. It usually means the mean and median are equal.

What Is This Calculator Useful For?

This calculator is ideal for:

  • Conducting exploratory data analysis

  • Detecting outliers

  • Summarizing key statistical properties

  • Creating data reports

  • Preparing data for inference and modeling

It’s a powerful tool in both academic and business data analysis settings.