Free Statistics Calculator with Steps
Calculate mean, median, mode, standard deviation, and more step-by-step. Learn statistics with instant feedback. Perfect for GCSE, A-Level, and university statistics.
Statistics Calculator
Calculate descriptive statistics with explanations
Step-by-step learning with explanations
Separate numbers with commas, spaces, or newlines. You can paste data from Excel or CSV.
Understanding Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset. They help us understand the central tendency (where data clusters) and spread (how data varies).
The three main measures of central tendency are mean (average), median (middle value), and mode (most frequent). Each has different uses depending on your data distribution.
Key Formulas
Measures of Central Tendency & Spread
Central Tendency
Mean: Sum ÷ count (affected by outliers)
Median: Middle value (resistant to outliers)
Mode: Most frequent (can be multiple)
Spread & Dispersion
Range: Difference between max and min
Variance: Average of squared deviations
Std Dev: Square root of variance
Position Measures
Q1: 25th percentile (lower quartile)
Q2: 50th percentile (median)
Q3: 75th percentile (upper quartile)
When to Use Each Measure
- • Mean: Normally distributed data without extreme outliers
- • Median: Skewed data or data with outliers
- • Mode: Categorical data or finding most common value
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the average (sum/count). Median is the middle value when sorted. Mode is the most frequent value. Each is useful for different types of data.
How do I calculate standard deviation?
Find the mean, subtract mean from each value and square, average the squared differences, then take the square root.
Population vs sample standard deviation?
Population SD divides by n. Sample SD divides by n-1 to account for estimating from a sample instead of the whole population.
How do I find the median with an even number of values?
Sort the data, find the two middle values, and calculate their average. For {2, 4, 6, 8}: median = (4+6)/2 = 5.
What are quartiles and IQR?
Quartiles divide data into four parts. IQR (Q3-Q1) measures the middle 50% spread and is resistant to outliers.
Is this suitable for GCSE statistics?
Yes! Covers all GCSE and A-Level statistics topics with step-by-step working showing the exact methods for exams.
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