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Statistics formulae

The 13 results the statistics notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 13, the formulae booklet prints 4 and 9 are yours to memorise.

Years 12-13 · 8 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

8 lessons

Sampling and the large data set

\frac{\text{stratum size}}{\text{population size}} \times \text{sample size}

NOT IN THE BOOKLET: LEARN ITConditionsNon-overlapping strata that between them cover the population; the numbers are then rounded to whole members.

Measures of location and spread

\text{mean: } \, \frac{Σ x}{n}

NOT IN THE BOOKLET: LEARN ITConditionsn ≥ 1.

σ^{2} = \frac{Σ x^{2}}{n} - (\frac{Σ x}{n})^{2}

IN THE FORMULAE BOOKLETConditionsThe variance of all n values treated as the population. An unbiased estimate of a population variance from a sample divides by n − 1 instead.

\text{mean}(x) = a + b \, \text{mean}(y), \qquad σ_{x} = |b|σ_{y}

NOT IN THE BOOKLET: LEARN ITConditionsCoding of the form x = a + by. The spread relation needs the magnitude of b: the standard deviation of x is |b| times that of y, whatever the sign of b.

Representing and interpreting data

\text{frequency density} = \frac{\text{frequency}}{\text{class width}}

NOT IN THE BOOKLET: LEARN ITConditionsGrouped continuous data drawn to the equal-area convention, with class widths in the same units throughout.

\text{outlier: beyond } Q_{1} - 1.5 \times \text{IQR} \text{ or } Q_{3} + 1.5 \times \text{IQR}

NOT IN THE BOOKLET: LEARN ITConditionsA convention rather than a definition. Use whichever rule the question states.

Probability and Venn diagrams

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

IN THE FORMULAE BOOKLETConditionsAny two events. For mutually exclusive events P(A ∩ B) is zero.

Conditional probability

P(A|B) = \frac{P(A ∩ B)}{P(B)}

NOT IN THE BOOKLET: LEARN ITConditionsP(B) > 0.

The binomial distribution

\text{P}(X = x) = \frac{1}{n}

NOT IN THE BOOKLET: LEARN ITConditionsA discrete uniform distribution: n listed outcomes, every one equally likely. Equal probabilities are the whole condition, so a total of two dice does not qualify.

P(X = x) = \, ^{n}C_{x} \, p^{x} (1 - p)^{n - x}

IN THE FORMULAE BOOKLETConditionsn fixed independent trials, two outcomes each, constant p; x = 0, 1, …, n.

The normal distribution

Z = \frac{X - μ}{σ}

NOT IN THE BOOKLET: LEARN ITConditionsX ~ N(μ, σ²) with σ > 0.

X ~ B(n, p) \, \approx \, N(np, \, np(1 - p))

NOT IN THE BOOKLET: LEARN ITConditionsn large with p not close to 0 or 1, so that np and n(1 − p) both comfortably exceed 5. A continuity correction is needed when moving to the normal.

Hypothesis testing: correlation and the normal

\text{mean of } n \text{ observations: } \, N(μ, \, σ^{2}/n)

IN THE FORMULAE BOOKLETConditionsA random sample of n independent observations from N(μ, σ²).

Every formula in the library is indexed by unit on the equation index, and the statistics notes are where these results are derived and used. The 9 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Vectors formulae · Mechanics formulae