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Scatter graphs

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Statistics


Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability


Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry


Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry


Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area


Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change


Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs


Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra


Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Double brackets: Expanding and factorising

Double and triple brackets - Higher

Solving equations

Expressions, equations, formulae, functions and identities

Writing formulae and equations from word problems

Writing formulae and equations from diagrams

Rearranging formulae

Factorising quadratics

The quadratic formula - Higher

Complete the square - Higher

Algebraic fractions - Higher

Sequences

Finding the nth term

Solving inequalities

Inequalities on graphs - Higher

Iteration - Higher

Simultaneous equations: elimination and substitution

Non-linear simultaneous equations - Higher

Algebraic proof - Higher

Composite and inverse functions - Higher

Number


Types of numbers

Order of operations: BODMAS

Multiplying and dividing by powers of 10

Multiplying and dividing whole numbers

Multiplying and dividing decimals

Negative numbers: add, subtract, multiply, divide

Prime numbers and prime factorisation

Multiples, factors and prime factors

LCM and HCF

Fractions

Fractions, decimals and percentages

Writing recurring decimals as fractions

Rounding: Integers, decimal places, significant figures

Estimation

Error intervals

Upper and lower bounds - Higher

Powers and roots: Square and cube numbers

Laws of indices: multiply, divide, brackets

Index laws: negative and fractional indices - Higher

Surds: Simplify, add and subtract - Higher

Rationalising surds - Higher

Standard form calculations

Explainer Video

Tutor: Alice

Summary

Scatter graphs

​​In a nutshell

A scatter graph is a graph displaying plotted data points.  The graph tells you how closely variables are related to each other as well as the kind of relation they have. 



Interpreting scatter graphs

Scatter graphs tell you about correlation between variables. They do not prove that one variable has an effect on another - correlation could happen because of a third factor or just by coincidence.


Definitions

Correlation

How closely two variables are related


Outliers

Points on the graph that do not fit the trend

Maths; Statistics; KS4 Year 10; Scatter graphs

Line of best fit

A straight line drawn through the middle of points, as close to each one as possible

Maths; Statistics; KS4 Year 10; Scatter graphs

Strong correlation

Points make a fairly straight line

Maths; Statistics; KS4 Year 10; Scatter graphs

Weak correlation

Points stray more from a straight line, but there is still positive or negative correlation

Maths; Statistics; KS4 Year 10; Scatter graphs

Negative correlation

Sloping downhill from left to right

Maths; Statistics; KS4 Year 10; Scatter graphs

Positive correlation

Sloping uphill from left to right

Maths; Statistics; KS4 Year 10; Scatter graphs

No correlation

Points have no pattern

Maths; Statistics; KS4 Year 10; Scatter graphs

​

​

Making predictions using scatter graphs

By drawing a line of best fit, you can make predictions using scatter graphs. It is important when drawing a line of best fit to ignore any outliers, as these could be potentially caused by an error that occurred during the experiment or when recording the data.


Tip: When drawing a line of best fit, make sure there are the same amount of points above the line as there are below.



Example 1

This scatter graph shows the correlation between the number of books read per year and age.

Maths; Statistics; KS4 Year 10; Scatter graphs


Draw a line of best fit and predict how many books per year a thirty-five year old would read.

Maths; Statistics; KS4 Year 10; Scatter graphs

Reading up and along, you can predict that a thirty-five year old would read 16‾\underline {16 }16​ books a year.


Note: In the example above, the line of best fit has been 'extrapolated' to make a prediction about the future.


​

Accuracy of predictions

Extrapolation

A type of estimation which goes outside the original range of observed or recorded values, based on the trends in the previous results.


Whilst this does provide a useful prediction, it is not always reliable as you have no way of knowing whether the current trend in data will remain the same.




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Representing data: Graphs and charts

Representing data: Graphs and charts

Scatter graphs

Scatter graphs

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FAQs - Frequently Asked Questions

What is weak correlation?

Weak correlation is where the points plotted stray more from a straight line, but there is still positive or negative correlation.

What is strong correlation?

Strong correlation is where the points make a fairly straight line.

What is a line of best fit?

A line of best fit is a straight line drawn through the middle of points, as close to each one as possible.

What is an outlier point?

Outlier points are points on the graph that do not fit the trend.

What is a scatter graph?

A scatter graph is a graph showing plotted points that tells you how closely things are related to each other as well as the kind of relation they have.

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