Formulae

All key GCSE Statistics formulae — 20 formulae organised by topic

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Averages

Mean

x̄ = Σx / n

Sum of all values divided by the number of values

Mean from Frequency Table

x̄ = Σfx / Σf

Sum of (frequency × value) divided by total frequency

Estimated Mean (Grouped Data)

x̄ = Σfm / Σf

Where m is the midpoint of each class interval

Dispersion

Range

Range = Max − Min

Difference between the largest and smallest values

Interquartile Range

IQR = Q₃ − Q₁

Difference between upper and lower quartiles

Standard Deviation

Higher

σ = √(Σ(x − x̄)² / n)

Square root of the mean of squared deviations from the mean

Variance

Higher

σ² = Σ(x − x̄)² / n

Mean of squared deviations from the mean

Standardised Score

Higher

z = (x − x̄) / σ

Number of standard deviations a value is from the mean

Probability

P(A) = favourable outcomes / total outcomes

Theoretical probability of event A occurring

Complementary Events

P(A') = 1 − P(A)

Probability of event A NOT occurring

Addition Rule (Mutually Exclusive)

P(A or B) = P(A) + P(B)

For mutually exclusive events A and B

Multiplication Rule (Independent)

P(A and B) = P(A) × P(B)

For independent events A and B

Conditional Probability

Higher

P(A|B) = P(A and B) / P(B)

Probability of A given that B has occurred

Expected Frequency

E = P(A) × n

Expected number of times event A occurs in n trials

Correlation

Spearman's Rank Correlation Coefficient

Higher

rₛ = 1 − (6Σd²) / (n(n²−1))

Measure of rank correlation; d = difference in ranks

Sampling

Capture-Recapture

N = (M × n) / m

N = population estimate, M = first catch, n = second catch, m = recaptured marked

Index Numbers

Index Number

Higher

Index = (Current value / Base value) × 100

Measures change relative to a base period (base = 100)

Rates

Crude Rate

Higher

Crude Rate = (Number of events / Population) × 1000

Rate per thousand of population

Time Series

Moving Average

MA = (x₁ + x₂ + ... + xₙ) / n

Average of n consecutive values to smooth out trends

Diagrams

Frequency Density

Frequency Density = Frequency / Class Width

Used for histograms with unequal class widths