Interpreting data
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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
Trigonometry
Angles and geometry
Shapes and area
Properties of 2D shapes
Congruence: conditions for congruent triangles
Similar shapes: Scaling
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Area and perimeter: Formulae
Area and circumference of circles: Formulae
3D shapes: faces, edges, vertices
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Volume of 3D shapes: Comparing, rates of flow
Area and volume scale factors
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Ratio proportion and rates of change
Graphs
Coordinates and midpoints
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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
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Double and triple brackets - Higher
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Writing formulae and equations from word problems
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Number
Types of numbers
Order of operations: BODMAS
Multiplying and dividing by powers of 10
Multiplying and dividing whole numbers
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Negative numbers: add, subtract, multiply, divide
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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
Summary
Interpreting data
In a nutshell
When given any kind of diagram showing a collection of data, it's important to be able to interpret the information. Diagrams could be misleading, averages could be affected by outliers - there are lots of things that can affect the data.
Misleading diagrams
Definition
A misleading diagram is one that gives information in a way that makes it seem like something it isn't.
When drawing your own diagrams to show data, there are set rules that you must follow such as having an equal scale and labelling the axis. It's important to notice when these things are missing so that you can be aware if they are misleading.
Example 1
This line graph is misleading for many reasons. List three things wrong with the graph.
1. The 'temperature' axis has an inconsistent scale - it does not go up in equal increments.
2. There is no label on the x-axis.
3. There is no title - this line graph could be showing anything!
This graph shows average temperatures each month. What is misleading about the change in temperature from February to April?
The line graph shows a straight line suggesting that the temperature changed evenly each month. However the scale tells us that from February to March there was an increase of , whereas from March to April there was a huge increase of !
Outliers resulting in a misleading mean and range
Another thing that can result in misleading information is an outlier - a data value that does not fit the general trend. Since they are far off the rest of the data, they lead to the mean and range becoming much smaller or bigger than they should be.
Example 2
Sarah records the number of books she reads every month for a year. The results are as follows:
Which value is the outlier?
Pick the value that does not seem to fit with the rest.
Calculate the mean and average both with and without the outlier.
| With the outlier | Without outlier |
| Mean: Add up all the values and divide by the frequency. Range: Minus the smallest value from the largest. | Mean: Add up all the values and divide by the frequency. Range: Minus the smallest value from the largest.
|
Notice how, without the outlier, the mean and range are both much smaller and in fact, much less misleading too.
FAQs - Frequently Asked Questions
What is an outlier?
An outlier is a data value that does not fit the general trend.
How can I tell if a diagram is misleading?
When drawing your own diagrams to show data, there are set rules that you must follow such as having an equal scale and labelling the axis. It's important to notice when these things are missing so that you can be aware if they are misleading.
What is a misleading diagram?
A misleading diagram is one that gives information in a way that makes it seem like something it isn't.