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Statistics basics flashcards

Averages, spread, chance, samples and tests in plain words, so you can read numbers and not be fooled by them.

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Beginner friendly, starts from zero
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Statistics basicsStart from zero · 1 of 11

What is statistics, in one plain sentence?

Statistics is the study of collecting numbers, summing them up, and deciding how far you can trust what they seem to say.

Numbers in, honest conclusions out.
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What you will learn

  1. Start from zero

    • What statistics is4 cards
    • The key words5 cards
    • Getting started2 cards

  2. Core basics

    • Averages3 cards
    • Spread3 cards
    • Kinds of data and their shapes5 cards
    • Chance3 cards
    • Links and causes2 cards

  3. Next steps

    • From sample to population4 cards
    • Testing ideas6 cards
    • Experiments2 cards
    • Regression and Bayes5 cards

  4. Go deeper

    • Traps in the data5 cards
    • Testing traps4 cards
    • Choosing the right measure4 cards
    • Reporting honestly4 cards

Final test and certificate

10 questions drawn fresh from the whole topic, about 15 minutes. Sign in, score 80% or more and get a free certificate with your name and a public check link anyone can open, such as an employer or a teacher. Not signed in? Try a practice test from the cards.

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About these cards

  • Reviewed 26 October 2026
  • CoversPython 3.13 statistics moduleSciPy 1.18
How these cards are made

Statistics basics at a glance

Statistics is the skill of learning true things from numbers, and knowing how sure you can be.

Tasting one spoon of soup tells you about the whole pot, if you stirred it first. Statistics is about tasting well and knowing when one spoon is not enough.

Words you will meet

Data
The numbers or facts you collected, like heights or test marks
Average
A single number that sums up a typical value; mean and median are two kinds
Spread
How far the numbers are from each other and from the average
Sample
The smaller group you actually measured
Population
The whole group you want to know about
Probability
How likely something is, from 0 (never) to 1 (certain)
Distribution
The pattern of how often each value shows up
Variable
One thing you measure that changes from person to person, like age

The steps

  1. 1. Start from zero (11 cards): What statistics is for, where you meet it every day, and the plain words the rest of the topic uses.
  2. 2. Core basics (16 cards): Averages, spread, shapes of data, basic chance and the difference between a link and a cause.
  3. 3. Next steps (17 cards): Samples, confidence, tests and regression: the statistics used to make real decisions.
  4. 4. Go deeper (17 cards): Paradoxes, biases, robust methods and testing traps that experienced analysts watch for.
All 11 cards in Start from zero
What is statistics, in one plain sentence?
Statistics is the study of collecting numbers, summing them up, and deciding how far you can trust what they seem to say.
Why does anyone need statistics?
Because we can rarely measure everyone or everything. Statistics lets us learn from a part and say how sure we are, instead of guessing.
Where do you meet statistics in a normal week?
Cricket batting averages, exam ranks, "70 percent chance of rain", product star ratings, election polls and price rise news are all statistics.
What everyday thing is a sample like?
Tasting one spoon of soup. If you stirred the pot, one spoon tells you about the whole pot. If you did not stir, the spoon can fool you.
What are a sample and a population?
The population is the whole group you care about, like every voter in a country. The sample is the smaller group you really asked, like 2,000 voters.
What is an average, and why are there different kinds?
An average is one number that stands for a typical value. The mean adds everything and divides; the median is the middle value. They can tell different stories.
What does spread mean?
Spread is how scattered the numbers are. Two classes can both average 60 marks, but one has everyone near 60 and the other has many 20s and many 100s.
What is probability?
Probability is how likely something is, from 0 (never) to 1 (always). A fair coin landing heads has probability 0.5, which is the same as 50 percent.
What are a variable and a distribution?
A variable is one thing you measure, like height. Its distribution is the pattern of how often each value appears: many people near the middle height, few very short or very tall.
What do you need before starting?
Only school maths: adding, dividing and percentages. A calculator, a spreadsheet or Python can do the heavy sums later.
What will you be able to do after this topic?
Choose the right average, describe spread, explain samples and chance, read test results and confidence intervals, and catch common tricks in charts and claims.
Statistics basics cheatsheet

Describe data

  • Mean Sum divided by count; pulled by outliers
  • Median Middle value; robust
  • Mode Most common value; for categories
  • Standard deviation Typical distance from the mean
  • IQR = Q3 - Q1 Spread of the middle half
  • z = (x - mean) / sd Distance in standard deviations

Chance

  • P(A and B) = P(A) x P(B) Only if independent
  • P(A or B) = P(A) + P(B) - P(A and B) Do not double count
  • P(A | B) Chance of A given B
  • Bayes: P(A|B) = P(B|A) P(A) / P(B) Update with base rate
  • 68 / 95 / 99.7 Normal: 1, 2, 3 sd

Inference

  • SE = sd / sqrt(n) Spread of the sample mean
  • 95% CI = mean +/- 1.96 x SE Large sample interval
  • Margin for a poll ~ 1 / sqrt(n) n = 1,000 gives about 3 points
  • p-value How surprising data are if no effect
  • alpha = 0.05 Accepted false alarm rate
  • Power = 0.8 Usual chance to detect a real effect

Which test

  • Two means Welch t-test
  • Two skewed groups Mann-Whitney U
  • Counts in a table Chi-square test
  • Two proportions z-test for proportions
  • Link between numbers Pearson or Spearman correlation
  • Any statistic, no formula Bootstrap interval

Python

  • statistics.median(xs) Median, standard library
  • statistics.quantiles(xs, n=4) Quartiles
  • scipy.stats.ttest_ind(a, b, equal_var=False) Welch t-test
  • scipy.stats.chi2_contingency(table) Chi-square test
  • scipy.stats.bootstrap((x,), np.median) Bootstrap CI
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