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Representation of data

Comparing data sets

Comparing data sets

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Further kinematics

Vector methods with projectiles
Variable acceleration in one dimension
Differentiating vectors
Integrating vectors

Application of forces

Static particles
Modelling with statics
Friction with static particles
Statics of rigid bodies
Dynamics and inclined planes
Connected particles

Projectiles

Horizontal projection
Projectiles: Horizontal and vertical components
Projection at any angle
Equation of the trajectory of a projectile

Forces and friction

Resolving forces
Inclined planes
The coefficient of friction

Moments

Moments
Resultant moments
Equilibrium
Centre of mass
Tilting
Laminas

Forces and motion

Force diagrams
Forces as vectors
Forces and acceleration
Motion in two dimensions
Connected particles
Pulleys

Variable acceleration

Functions of time: Displacement, velocity, acceleration
Using differentiation to find velocity and acceleration
Maxima and minima problems
Using integration to find velocity and displacement
Constant acceleration formulae

Constant acceleration

Displacement-time graphs
Velocity-time graphs
Constant acceleration: Deriving formulae
Constant acceleration formulae: SUVAT
Vertical motion under gravity

Modelling in mechanics

Modelling assumptions
Quantities and units in mechanics
Working with vectors

Normal distribution

The normal distribution
The normal distribution: Finding probabilities
The inverse normal distribution function
The standard normal distribution
Finding the mean and standard deviation
Normal approximation to the binomial distribution
Hypothesis testing with the normal distribution

Conditional probability

Set notation
Conditional probability
Conditional probability in Venn diagrams
Probability formulae
Conditional probability: Tree diagrams

Correlation and hypothesis testing

Exponential models
Measuring correlation
Hypothesis testing for zero correlation

Hypothesis testing I

Hypothesis testing
Hypothesis testing: Finding critical values
One-tailed tests
Two-tailed tests

Binomial distribution

Probability distributions
The binomial distribution
Cumulative probabilities

Probability

Calculating probabilities
Venn diagrams
Probability: Mutually exclusive and independent events
Probability: Tree diagrams

Representation of data

Outliers
Box plots
Cumulative frequency
Histograms
Comparing data sets
Correlation
Linear regression

Measures of location and spread

Measures of central tendency: Mean, median, mode
Measures of spread: Range
Variance and standard deviation

Data collection

Population and samples
Sampling techniques
Types of data

Vectors II

3D coordinates
Vectors in 3D
Solving geometric problems
Applications to mechanics: 3D vectors

Numerical methods

Locating roots
Iteration
Staircase and cobweb diagrams
Newton-Raphson method
Numerical methods: Applications to modelling

Integration II

Integrating standard functions
Integrating f(ax + b)
Integration with trigonometric identities
Reverse chain rule
Integration by substitution
Integration by parts
Integration using partial fractions
Finding areas using integration
The trapezium rule
Solving differential equations
Modelling with differential equations

Differentiation II

Differentiating sin x and cos x
Differentiating exponentials and logarithmic functions
The chain rule
The product rule
The quotient rule
Differentiating inverse functions
Differentiating trigonometric functions
Parametric differentiation
Implicit differentiation
Second derivatives: Concave and convex functions
Connected rates of change

Trigonometry and modelling

Addition formulae
Using the angle addition formulae
Double angle formulae
Solving trigonometric equations: Double angle formula
Simplifying a cos x + b sin x
Proving trigonometric identities
Modelling with trigonometric functions

Trigonometric functions

Secant, cosecant and cotangent
Graphs of sec x, cosec x and cot x
Solving equations with sec x, cosec x and cot x
Further trigonometric identities
Inverse trigonometric functions

Radians

Radian measure
Arc length
Areas of sectors and segments
Solving trigonometric equations
Small angle approximations

Sequences and series

Sequences revision
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
Sum to infinity
Sigma notation
Modelling with sequences and series

Binomial expansion II

Binomial expansion: (1+x)^n
Binomial expansion: (a+bx)^n
Binomial expansion with partial fractions
Binomial expansion of compound expressions

Parametric equations

Parametric equations
Using trigonometric identities
Sketching parametric curves
Points of intersection of parametric curves
Modelling with parametric equations

Functions

Functions and mappings
Composite functions
Inverse functions
The modulus function
y = |f(x)| and y = f(|x|)
Combining transformations
Solving modulus equations
Modulus inequalities

Algebraic fractions

Operations with algebraic fractions
Partial fractions
Repeated factors
Algebraic division

Proof II

Proof by contradiction
Criticising proofs

Vectors I

Vectors
Representing vectors
Magnitude and direction of a vector
Position vectors and displacement vectors
Solving geometric problems
Modelling with vectors

Integration I

Integrating x^n
Indefinite integrals
Finding functions by integrating
Definite integrals
Area under a curve
Area under the x-axis
Area between a curve and a line

Differentiation I

Finding the gradient of a curve
Differentiation from first principles
Differentiating x^n
Differentiating functions with multiple terms
Gradients, tangents and normals
Increasing and decreasing functions
Second order derivatives
Stationary points
Sketching gradient functions
Modelling with differentiation

Exponentials and logarithms

Exponential functions
y = e^x
Exponential modelling
Logarithms
Laws of logarithms
Solving equations using logarithms
Natural logarithms
Logarithms and non-linear data
Harder exponential modelling

Trigonometric equations

Angles in all four quadrants
Exact trigonometric values
Trigonometric identities
Simple trigonometric equations
Harder trigonometric equations
Equations and identities

Trigonometry

The cosine rule
The sine rule
Area of a triangle
Solving triangle problems
Trig graphs: sin x, cos x, tan x
Transforming trigonometric graphs

Binomial expansion I

Pascal's triangle
Factorial notation
Binomial expansion
Solving binomial problems
Binomial estimation

Circles

Midpoints and perpendicular bisectors
Equation of a circle
Intersection of straight lines and circles
Using tangent and chord properties
Circles and triangles
Intersection of two circles

Straight line graphs

y = mx + c
Equations of straight lines
Parallel and perpendicular lines
Length and area
Modelling with straight lines

Transformations

Translating graphs
Stretching and reflecting graphs
Transforming graphs

Sketching graphs

Cubic graphs
Quartic graphs
Reciprocal graphs
Points of intersection
Using the discriminant
Direct and inverse proportion

Polynomials

Functions
Expanding brackets
Factorising
Simplifying algebraic fractions
Polynomial division
The factor theorem

Equations and inequalities

Linear simultaneous equations
Quadratic simultaneous equations
Set notation and interval notation
Linear inequalities
Quadratic inequalities
Inequalities on graphs
Inequality regions

Quadratics

Solving quadratic equations
Completing the square
Quadratic graphs
Identifying the discriminant
Solving disguised quadratics

Indices and surds

Laws of indices
Negative and fractional indices
Surds
Rationalising the denominator

Proof I

Mathematical structure and arguments
Disproof by counterexample
Proof by deduction
Proof by exhaustion

Explainer Video

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Tutor: Alice

Summary

Comparing data sets

In a nutshell

Data can be compared in two ways: measures of location and measures of spread.



Measures of location

To compare data using measures of location, you can use the mean or the median.



Measures of spread

To compare data using measures of spread, you can use the standard deviation or the interquartile range.



Comparing data

When comparing data, you must compare a measure of location and a measure of spread.

You can either compare the means and the standard deviations or the medians and the interquartile ranges - the latter of which is preferred if the given data has extreme values.


Example 1

Katie averaged 3.63.63.6 hours of reading last month, with a standard deviation of 0.20.20.2hours.

Knowing that the average reading time for someone her age is 1.41.41.4 hours with a standard deviation of 0.50.50.5 hours, compare Katie's reading time to the average.


Katie averaged more reading time than people her age. However, her values are less spread than the average.

​



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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Representing data: Graphs and charts

Unit 1

Representing data: Graphs and charts

Interpreting data

Unit 2

Interpreting data

Jump Ahead

Score 80% to jump directly to the final unit.

Optional

Comparing data sets

Unit 3

Comparing data sets

Final Test

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FAQs - Frequently Asked Questions

Which measures of spread can be used when comparing data?

The standard deviation or the interquartile range.

Which measures of location can be used when comparing data?

The mean or the median.

How can data be compared?

Using measures of location or measures of spread.

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