Lesson

Counting outcomes, summarizing reality

Statistics is the art of summarizing data. Probability is the math of what could happen. Together, they let you reason under uncertainty — from polls to weather forecasts to medical trials.

Center

Mean is the average. Median is the middle value. Mode is what appears most often. Outliers tug the mean, leave the median alone.

Spread

Range = max − min. IQR = Q₃ − Q₁ (middle 50%). Standard deviation measures the typical distance from the mean.

Probability

For equally likely outcomes, P(event) = favorable / total. Probabilities are between 0 and 1 (or 0% and 100%).

Independence

Events are independent if one's outcome doesn't affect the other. For independent A and B: P(A and B) = P(A) × P(B).

Key formulas

Mean

Σxᵢ / n

Variance

Σ(xᵢ − x̄)² / n

Std deviation

σ = √variance

P(event)

favorable / total

P(A or B)

P(A) + P(B) − P(A and B)

P(A and B) — indep.

P(A) × P(B)

Complement

P(not A) = 1 − P(A)

Permutations

nPr = n! / (n−r)!

Combinations

nCr = n! / (r! (n−r)!)

Empirical rule

68 / 95 / 99.7 (1, 2, 3 σ)

Hands-on tools

Roll dice, build a histogram, fit a regression line, or branch a probability tree.

Coin / dice / spinner simulator

Run many trials and watch the bar chart converge toward the theoretical probability (Law of Large Numbers).

Trials so far: 0.

Build a histogram

Type a comma-separated list of numbers — see mean, median, range, IQR live.

Bins

Scatter plot & regression line

Pick a data set and toggle the best-fit line. Shows correlation r and the line equation.

Probability tree

Two events in sequence — products on the leaves sum to 1.

P(A) 0.6

P(B | A) 0.7

Quiz

Score 0/0 Streak 🔥 0 Best 0

Flashcards

Tap to flip. ← / → keys to navigate.

Mean

MeanArithmetic average; sum divided by count.

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Daily challenge

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For teachers

Print-ready worksheet, answer key, teaching tips and standards alignment.

Teaching tips

Standards alignment

Reference

Formula sheet

Mean

x̄ = Σxᵢ / n

Median

middle value (sorted)

Mode

most frequent value

Range

max − min

IQR

Q₃ − Q₁

Variance

σ² = Σ(xᵢ − x̄)² / n

Std deviation

σ = √(σ²)

P(event)

favorable / total

P(A or B)

P(A) + P(B) − P(A∩B)

P(A and B) indep

P(A)·P(B)

Complement

P(Aᶜ) = 1 − P(A)

Conditional

P(A|B) = P(A∩B)/P(B)

nCr

n! / (r! (n−r)!)

nPr

n! / (n−r)!

Empirical rule

~68 / 95 / 99.7

Photo gallery

Images sourced from Wikipedia.

Counting outcomes, summarizing reality

Center

Spread

Probability

Independence

Key formulas

Hands-on tools

Coin / dice / spinner simulator

Build a histogram

Scatter plot & regression line

Probability tree

Quiz

Flashcards

Daily challenge

For teachers

Teaching tips

Standards alignment

Reference

Formula sheet

Photo gallery

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