Statistics guides
Analyze data with mean, median, mode, standard deviation, and probability distributions.
17 guides · each with a free step-by-step calculator
Statistics Solver: Master Data Analysis with Step-by-Step Solutions
Five friends earn 30, 32, 35, 38 and 40 thousand a year. A millionaire joins the group and suddenly the 'average' salary jumps above 100 thousand. Nobody got a raise. This guide shows you how mean, median, mode and standard deviation really work, and which one to trust.
Distribution Calculator: Understanding Normal Distribution & Probability Calculations
You scored 85 on a test where the average was 70. Is that good, or just okay? It depends on how spread out everyone else's scores were. In this guide you'll learn the bell-shaped normal distribution, the 68-95-99.7 rule and z-scores, so you can compare any score fairly.
How to Find the Average (Mean) of Numbers
You scored 72, 85 and 90 on three tests. So how did you really do this term? One number can answer that: the average. In this guide you'll learn how to find it in seconds, and when the average can trick you.
Normal Distribution Formula Explained Simply
Why are most people close to average height, with very few giants? Heights, test scores and measurement errors all follow the same bell-shaped pattern. This guide explains the normal distribution, its formula, and how to read the answer correctly.
How to Find the Median (Step-by-Step Guide)
Why do news reports say median house price instead of average house price? Because one mansion can make the average look silly. In this guide you'll learn how to find the median for odd and even lists, and when it beats the mean.
How to Find the Mode of a Data Set
Which shoe size should a shop order the most of? Not the average size, because nobody wears size 8.2. The answer is the mode. This guide shows you how to find it, what to do with ties, and what no mode means.
Partner Spotlight
How to Calculate Standard Deviation (Easy)
Two classes both average 70 marks. In one, everyone scored 65 to 75. In the other, scores ran from 30 to 100. Same average, very different story. Standard deviation measures that difference, and this guide shows you how to calculate it by hand.
How to Calculate Probability (With Examples)
What are your chances of rolling a 6, drawing an ace, or winning a lucky draw? Every one of these questions uses the same simple formula. In this guide you'll learn to calculate probability, write it as a fraction, decimal or percentage, and avoid the classic traps.
What Is a Factorial? (n!) Explained Simply
How many ways can you shuffle a deck of 52 cards? The answer has 68 digits, far more than the number of grains of sand on a beach. That number is 52 factorial. In this guide you'll learn what n! means, how to work it out, and why 0! equals 1.
Combinations (nCr) Formula Explained Simply
Why is winning a 6-from-49 lottery so hard? Because there are 13,983,816 different ways to pick the numbers. Counting groups like this is what combinations do. In this guide you'll learn the nCr formula, a fast shortcut, and how to tell combinations from permutations.
nPr Formula: Permutations Explained Simply
Eight runners, three medals. How many different podiums are possible? More than 300. Questions like this, where order matters, are permutations. In this guide you'll learn the nPr formula, a quick countdown shortcut, and how to tell nPr from nCr.
How to Calculate Variance (Step-by-Step)
Two seedling trays have the same average height, but one looks neat and the other looks messy. How do you measure messy? With variance. This guide shows you how to calculate it step by step, and the difference between population and sample variance.
Partner Spotlight
How to Find the Range in Math (Easy Guide)
How much did the temperature swing this week? How far apart were the best and worst scores in your class? One subtraction answers both. In this guide you'll learn how to find the range, what it tells you, and when it can mislead you.
How to Calculate a Weighted Average
You scored 85 on homework and 72 on the exam. Is your grade 78.5? Not if the exam counts for more. Schools, shops and investors all use weighted averages to get fair answers. This guide shows you how to calculate one in four quick steps.
What Is a Z-Score? Formula and Examples
You got 80 in maths and 85 in English. Which result is actually better? It depends on how everyone else did. A z-score answers that by putting any score on one fair scale. This guide shows you how to calculate it and what the number means.
Binomial Probability Formula Explained Simply
Flip a fair coin 10 times. What is the chance of exactly 5 heads? Most people guess 50%, but the real answer is under 25%. This guide explains the binomial formula that gives the right answer, and how to use it for any repeated yes-or-no trial.
How to Calculate a Confidence Interval
A poll says 52% ± 3%. Where does that ± 3% come from? It is a margin of error, and it turns one guess into an honest range. In this guide you'll learn how to calculate the margin of error and a confidence interval for a mean, step by step.
