Higher Applications of Mathematics
Quick reference cards for probability, diagrams, averages, spread, regression, confidence intervals and hypothesis tests.
A measure of chance between 0 and 1.
Use when describing likelihood or calculating expected frequency.
P(event) = favourable outcomes / total outcomes.
P(rain) = 0.3 means rain is expected on about 30% of similar days.
A branch diagram for multi-stage events.
Use when outcomes happen in stages, such as two selections or two tests.
Multiply along branches; add separate branches for 'or'.
P(pass both) = P(pass first) x P(pass second).
A diagram showing overlap between sets.
Use when categories overlap, such as pupils studying French and Spanish.
Fill the intersection first, then the rest of each set.
If 12 study both, place 12 in the overlap.
The arithmetic average.
Use for a typical value when data has no strong outliers.
mean = total / number of values.
2, 5, 8 has mean 15 / 3 = 5.
The middle value when data is ordered.
Use when data is skewed or has outliers.
Order values and find the middle.
2, 5, 20 has median 5.
A measure of spread around the mean.
Use to compare consistency between data sets.
Higher standard deviation means more variability.
A lower sd for journey times means times are more consistent.
The spread of the middle 50% of data.
Use with medians and box plots.
IQR = upper quartile - lower quartile.
Q3 = 18 and Q1 = 11 gives IQR = 7.
A diagram showing median, quartiles, range and outliers.
Use to compare distributions quickly.
Compare medians for centre and IQRs for spread.
A higher median box plot suggests generally larger values.
A graph for grouped continuous data.
Use when data is grouped into intervals.
Compare shape, skewness and modal class.
A right-skewed histogram has a long tail to the right.
A graph of paired numerical data.
Use to look for relationships between two variables.
Look for direction, strength and unusual points.
Revision time and score may show positive association.
A measure of strength and direction of a linear relationship.
Use with paired numerical data.
r is between -1 and 1; correlation does not prove causation.
r = 0.82 suggests a strong positive correlation.
A straight-line model for prediction.
Use when a linear relationship is reasonable.
Interpret gradient as change in y for each 1-unit increase in x.
A gradient of 2.5 means y increases by about 2.5 per x.
A range of plausible values for a population parameter.
Use when estimating from sample data.
Wider intervals mean less precise estimates.
A mean time interval of 24 to 30 minutes suggests the true mean may lie in that range.
A method for judging evidence against a claim.
Use when deciding whether sample data gives evidence of a difference or effect.
Compare p-value with significance level.
If p < 0.05, there is evidence against the null hypothesis.
A test involving means.
Use for testing a mean or comparing means from sample data.
Use p-value to decide evidence.
A small p-value suggests the mean differs from the claim.
A t-test for matched before/after data.
Use when the same people or items are measured twice.
Test the mean of the paired differences.
Before and after fitness scores for the same pupils are paired.
A test comparing two sample proportions.
Use for success/failure outcomes in two groups.
Compare the p-value with the significance level.
Compare the proportion passing in two classes.