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Frequency Polygons

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Area Between Two Curves
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- 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 Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
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- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
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- Limit of a Sequence
- Limits
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- Limits of a Function
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- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
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- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Radius of Convergence
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Separation of Variables
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
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- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
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- Theorems of Continuity
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- Composition
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- Coordinate Systems
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- Fundamentals of Geometry
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- HL ASA and AAS
- Identity Map
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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
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- Pythagoras Theorem
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- Mechanics Maths
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- Assumptions
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- Power
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- Variable Acceleration
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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
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- Quartiles and Interquartile Range
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- Pure Maths
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- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
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- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
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- Approximation and Estimation
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- Area and Perimeter of Quadrilaterals
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- Argand Diagram
- Arithmetic Sequences
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- Bijective Functions
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- Circle Theorems
- Circles
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- Combination of Functions
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- Completing the Square
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- Complex Numbers
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- Coordinate Geometry
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- Data transformations
- De Moivre's Theorem
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- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
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- Differentiation
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- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
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- Distance from a Point to a Line
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- 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
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- 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 Matrices
- 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
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- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
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- Rates of Change
- Ratio
- Ratio Fractions
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- 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
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- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
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- Simultaneous Equations
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- Small Angle Approximation
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- 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
- Sum of Natural Numbers
- 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
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- Trigonometry
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- Unit Circle
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- Variables in Algebra
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- Verifying Trigonometric Identities
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- Statistics
- Bias in Experiments
- Binomial Distribution
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- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Distribution Function
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Degrees of Freedom
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
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- Inference for Distributions of Categorical Data
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- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
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- Variance for Binomial Distribution
- Venn Diagrams

A **frequency polygon **is a graphical representation of a data set with frequency information. It is one of the most common statistical tools used to represent and analyse **grouped statistical data.**

The use of a frequency polygon has been shown to be very useful for trend analysis and data recall.

Below is an example of a frequency polygon.

Example of a frequency polygon, Nilabhro Datta - StudySmarter Originals

The value of the data point is plotted along the horizontal axis, and the frequency corresponding to each data point is plotted along the vertical axis. So from the above graph, we can deduce that for x = 10, frequency = 8. We will explore further nuances of frequency polygons later on.

Given a grouped frequency distribution, follow the following steps to draw the corresponding frequency polygon.

1) Find the **class mark **for each class interval of the frequency distribution. To make it easier, you can add another column to the frequency distribution to note down the class marks.

class mark =

2) Plot the **class marks **along the horizontal axis and the **frequencies **along the vertical axis.

3) For each class mark, plot the frequency corresponding to that class on the graph.

4) Join all the plotted points in sequential order (connect the first point with the second, then the second to the third, and so on ...)

5) The resulting figure is the necessary frequency polygon.

Draw the frequency polygon graph for the following frequency distribution:

Class | frequencies |

5-7 | 15 |

7-9 | 18 |

9-11 | 28 |

11-13 | 7 |

13-15 | 22 |

15-17 | 35 |

First, let's find the class mark for each class. We can show the results in the following table:

Class | Class Mark | frequencies |

5-7 | 6 | 15 |

7-9 | 18 | |

9-11 | 10 | 28 |

11-13 | 12 | 7 |

13-15 | 14 | 22 |

15-17 | 16 | 35 |

Now that we have all the class marks and the corresponding frequencies, we can plot the points on the graph taking the class marks on the horizontal axis and the frequencies on the vertical axis.

Finally, we have to join the plotted points sequentially.

The above diagram is our final frequency polygon.

Here are a few things to be mindful of when creating your own frequency polygon:

Make sure you use the class mark and not the class limits to plot the graph.

Sometimes you may want to obtain a closed polygon. In such cases, you could extrapolate the classes to the expected next class in either direction and consider the frequency of each class to be 0. In the above example, this would mean adding the classes (4, 0) and (18, 0) – since the expected next class mark on the left-hand side is 4 and on the right-hand side is 0.

Frequency polygons share many similarities with Histograms. Both histograms and frequency polygons are used to graphically represent frequency distribution. While frequency polygons can be drawn with or without a corresponding histogram, it is very easy to obtain a frequency polygon from a given histogram.

**To draw a frequency polygon from a given histogram, join the middle of the top of each bar of the histogram sequentially. **

This is effectively equivalent to the same process that we followed to draw our frequency polygon. The horizontal middle of the bar of a histogram is the class mark, and the top of the histogram is the corresponding frequency. Thus the middle of the top of each bar gives the point to plot on the graph, and by joining these points we get the frequency polygon.

In the above example, the frequency polygon is obtained by joining the middle of the top of each bar of the histogram sequentially.

A frequency polygon is a graphical representation of a data set with frequency information. It is one of the most common statistical tools used to represent and analyse grouped statistical data.

To draw a frequency polygon from a given grouped frequency distribution, we must plot the frequency against the class marks and not the class boundaries.

While frequency polygons can be drawn with or without a corresponding histogram, it is very easy to obtain a frequency polygon from a given histogram.

To draw a frequency polygon, follow the following steps:

1) Find the class mark for each class interval of the frequency distribution.

Class mark = (upper limit + lower limit)/2

2) Plot the class marks along the horizontal axis and the frequencies along the vertical axis.

3) For each class mark, plot the frequency corresponding to that class on the graph.

4) Join all the plotted points in sequential order (connect the first point with the second, then the second to the third, and so on…)

5) The resulting figure is the necessary frequency polygon.

More about Frequency Polygons

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