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Box Plots

- Calculus
- Absolute Maxima and Minima
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Arithmetic Series
- Average Value of a Function
- Candidate Test
- Combining Differentiation Rules
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Disk Method
- Divergence Test
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Improper Integrals
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrating Even and Odd Functions
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
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- Limits of a Function
- Linear Differential Equation
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- Maclaurin Series
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- One-Sided Limits
- Optimization Problems
- P Series
- Particular Solutions to Differential Equations
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Tangent Lines
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
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- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
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- 3-Dimensional Figures
- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
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- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
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- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
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- Glide Reflections
- HL ASA and AAS
- Identity Map
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- Isometry
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- Law of Cosines
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- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
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- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
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- Converting Units
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- Kinematics
- Newton's First Law
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- Projectiles
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- Probability and Statistics
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- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
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- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
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- Composition of Functions
- Compound Interest
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- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
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- Data transformations
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
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- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal´s Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
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- Rounding
- SAS Theorem
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- Scale Drawings and Maps
- Scale Factors
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- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
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- Simple Interest
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- Simultaneous Equations
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- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
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- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Comparing Data
- Conditional Probability
- Correlation
- Cumulative Frequency
- Data Interpretation
- Discrete Random Variable
- Distributions
- Events (Probability)
- Frequency Polygons
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Testing
- Large Data Set
- Linear Interpolation
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Probability
- Probability Calculations
- Probability Distribution
- Probability Generating Function
- Quantitative Variables
- Random Variables
- Sampling
- Scatter Graphs
- Single Variable Data
- Standard Deviation
- Standard Normal Distribution
- Statistical Measures
- Tree Diagram
- Type I Error
- Type II Error
- Types of Data in Statistics
- Venn Diagrams

A box plot is a way of visually displaying data which shows different features of the data such as the lowest value, lower quartile, median, upper quartile, highest value, and any outliers that you may have in your data. Box plots can also be used to compare data, this can be done by placing more than one box plot onto the diagram.

Below is an example of a box plot, explaining what each part means.

Breakdown of a box plot, Thomas-Gay - StudySmarter OriginalsFrom a box plot you can then find out the interquartile range. This can be calculated by subtracting the lower quartile from the upper quartile.

For example, in the picture above the interquartile range would be

.

Knowing this can also help you identify any outliers, as an outlier is known to be any piece of data that is 1.5 the interquartile range **above** the upper quartile or 1.5 the interquartile range **below** the lower quartile.

Using the example above, to find out what would be a lower outlier you can simply calculate it. so this means that an outlier will be any piece of data less than 2.5, which is why the data piece marked as 1.5 is classed as an outlier.

In order to plot a box plot, you need the following,

Lowest value.

Lower quartile (Q

_{1}).Median (Q

_{2}).Upper quartile (Q

_{3}).Highest value.

You don't necessarily need an outlier in order to draw a box plot as there may not be any found in the data.

When you are asked to draw a box plot you may have data presented to you in a table or you may have each of the above features listed for you, let's work through both examples and how you would plot them.

When the data are given to you like this, you can simply draw your box plot without needing to do any calculations.

To create the box plot for this data, you would add a line at the suitable point for each feature and then connect them to create a box.

However, sometimes the data may not be presented clearly – you may be given a list of data, as given in the next example.

Here is a sample of test scores from a class quiz, 47, 50, 62, 76, 98, 54, 38, 66, 24, 82.

Represent the following set into a box plot.

**Solution**

24, 38, 47, 50, 54, 62, 66, 76, 82, 98

By doing this you can see that 24 is your lowest value and 98 is the highest value. To find the median you need to find the middle number, since there are 10 numbers you will need to take the midpoint of the two middle numbers:

Now you need to find your lower quartile and upper quartile. The lower quartile can be found by finding the midpoint between your lowest value and the median, and the upper quartile can be found by finding the midpoint between your midpoint of the highest value:

24, 38, 47, 50, 54, 62, 66, 76, 82, 98

You can see that the lower quartile is 47 and your upper quartile is 76.

Once you have gathered all of the information you are able to draw your box plot:

It is very important to understand how to interpret a box plot. You should know how to identify the different features that are presented in a box plot as well as using the information you are given to compare box plots. Below is an example of a box plot – let's take a look at it and work through some potential questions you may come across.

The box plot below shows the height of a group of boys,

Here are some examples of questions you may be asked about the box plot,

What are the lower and upper quartiles?

You know that the upper and lower quartiles are what make up the box, so you can see that the lower quartile is 160.5 and the upper quartile is 165.5.

Calculate the interquartile range

To do this you can take the lower quartile and subtract it from the upper quartile,

What is the median?

This can be identified by looking at the box plot and finding the middle line of the box, which is 163.

Box plots can also be used to compare data, for example, data representing the height of a group of girls can be placed below the original box plot to help you compare and contrast.

Here are some examples of questions you may be asked about the two box plots.

Compare the heights of males and females

For this question, you can describe what you can see on the box plots. The box plots show that males have a higher value and higher median than females, meaning that the males are taller.

What is the highest value of heights of females?

For this question you only need to look at the female box plot, it shows that the highest value is 163.

A person was measured at a height of 162cm, give a reason why they are more likely to be male or female?

For this question you will need to look at both of the box plots, you can see that there are much more males that had a height of 162 or higher, which means that it is more likely to be a male that was measured at 162.

A box plot is used to visually display certain features of data.

A box plot shows you the lowest value, lower quartile, median, upper quartile and the highest value, as well as any outliers there may be in the data.

An outlier can be described as a piece of data that is 1.5 x the interquartile range below the lower quartile or above the upper quartile.

You can draw more than one box plot on the scale to help you compare the data.

A box plot is a type of graph that visually displays certain features of data.

The median of your data can be found by identifying the middle line of the box plot.

More about Box Plots

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