Statistics Calculator

📊 Descriptive Statistics

Count (n)–
Sum–
Mean–
Median–
Min / Max–
Range–

📏 Spread & Quartiles

Sample Std. Deviation–
Sample Variance–
Q1 (25th percentile)–
Q3 (75th percentile)–
Interquartile Range (IQR)–

What Is a Statistics Calculator?

This statistics calculator computes a full set of descriptive statistics from a data set — count, sum, mean, median, range, standard deviation, variance, and quartiles — all in one place, useful for coursework, research, or data analysis.

How to Use the Statistics Calculator

  1. Enter your numbers, separated by commas or spaces.
  2. All statistics calculate instantly.

Key Formulas

Mean
Mean = Sum of values ÷ Count
Sample Standard Deviation
s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
Interquartile Range
IQR = Q3 − Q1
Q1 = median of the lower half of the data
Q3 = median of the upper half of the data

Worked Example

Example: 12, 15, 22, 8, 19, 30, 14, 25, 18, 21

Sorted: 8, 12, 14, 15, 18, 19, 21, 22, 25, 30

Count: 10, Sum: 184, Mean: 18.4

Median: (18+19)/2 = 18.5

Range: 30 − 8 = 22

Understanding Your Results

Quartiles divide sorted data into four equal parts. Q1 marks the boundary of the lowest 25% of values; Q3 marks the boundary of the highest 25%. The IQR (the middle 50% of the data) is a robust measure of spread that's less sensitive to outliers than the full range.

When to Use Each Statistic

  • Use mean and standard deviation for roughly symmetric data without extreme outliers.
  • Use median and IQR for skewed data or data with outliers, since they're more resistant to extreme values.
  • Use range for a quick, rough sense of overall spread.

Common Mistakes to Avoid

  • Reporting mean alone without any measure of spread (standard deviation, IQR, or range).
  • Using mean and standard deviation on heavily skewed data where median and IQR would be more representative.
  • Forgetting to sort the data before manually calculating quartiles or median.

Frequently Asked Questions

Typically: count, sum, mean, median, range, standard deviation, variance, and quartiles — everything this calculator computes at once.

IQR measures the spread of the middle 50% of your data and is commonly used to identify outliers (values falling far outside Q1 − 1.5×IQR to Q3 + 1.5×IQR).

Sort the data, then find the median of the lower half (Q1) and the median of the upper half (Q3); methods can vary slightly depending on whether the median itself is included in each half.

Median is more resistant to outliers and skewed data, since it's based on position rather than magnitude — useful for data like income or home prices where extreme values are common.

Variance is the average of squared deviations from the mean; standard deviation is its square root, expressed in the same units as the original data, which makes it easier to interpret.