Grade 10
  1. Number Systems  1.1. Real Numbers  1.1.1. Properties of Real Numbers  1.1.2. Rational and Irrational Numbers  1.1.3. Decimal Representation of Real Numbers  1.1.4. Operations on Real Numbers  1.1.5. Real Numbers on the Number Line  1.2. Euclid's Division Lemma  1.3. Prime Factorization  1.4. LCM and HCF  1.5. Exponents and Radicals  1.5.1. Laws of Exponents  1.5.2. Simplifying Radical Expressions  1.5.3. Scientific Notation
  2. Algebra  2.1. Polynomials  2.1.1. Definition and Types of Polynomials  2.1.2. Degree of a Polynomial  2.1.3. Zeros of a Polynomial  2.1.4. Factorization of Polynomials  2.1.5. Algebraic Identities  2.2. Linear Equations in Two Variables  2.2.1. Graph of Linear Equations  2.2.2. Solutions of Linear Equations  2.2.3. Application of Linear Equations in Word Problems  2.3. Quadratic Equations  2.3.1. Standard Form of a Quadratic Equation  2.3.2. Methods of Solving Quadratic Equations  2.3.2.1. Factorization Method  2.3.2.2. Completing the Square Method  2.3.2.3. Quadratic Formula  2.3.3. Nature of Roots  2.4. Arithmetic Progressions  2.4.1. Definition of Arithmetic Progression  2.4.2. General Term of an AP  2.4.3. Sum of First n Terms of an AP  2.5. Introduction to Functions  2.5.1. Definition and Types of Functions  2.5.2. Domain and Range  2.5.3. Composition of Functions  2.5.4. Inverse of a Function
  3. Coordinate Geometry  3.1. Cartesian System  3.2. Distance Formula  3.3. Section Formula  3.4. Area of a Triangle  3.5. Slope of a Line  3.6. Equation of a Line  3.6.1. Slope-Intercept Form  3.6.2. Point-Slope Form  3.6.3. Two-Point Form  3.6.4. Intercept Form  3.6.5. General Form of a Line
  4. Trigonometry  4.1. Trigonometric Ratios  4.1.1. Sine Cosine Tangent and their Reciprocals  4.1.2. Values of Trigonometric Ratios at Specific Angles  4.2. Trigonometric Identities  4.3. Trigonometric Ratios of Complementary Angles  4.4. Heights and Distances  4.4.1. Angle of Elevation and Depression  4.4.2. Applications in Real-Life Problems
  5. Geometry  5.1. Triangles  5.1.1. Congruence of Triangles  5.1.2. Criteria for Congruence  5.1.3. Properties of Triangles  5.2. Similarity  5.2.1. Similar Figures  5.2.2. Criteria for Similarity  5.2.3. Similarity of Triangles  5.2.4. Applications of Similarity in Real-Life  5.3. Circles  5.3.1. Properties of a Circle  5.3.2. Tangent to a Circle  5.3.3. Number of Tangents from a Point  5.3.4. Angle Subtended by an Arc  5.4. Constructions  5.4.1. Construction of Similar Triangles  5.4.2. Tangent to a Circle  5.4.3. Construction of Angle Bisectors
  6. Mensuration  6.1. Areas of Plane Figures  6.1.1. Area of a Triangle  6.1.2. Area of a Parallelogram  6.1.3. Area of a Trapezium  6.1.4. Area of a Rhombus  6.2. Surface Areas and Volumes  6.2.1. Surface Area of a Cube Cuboid and Cylinder  6.2.2. Surface Area of a Cone and Sphere  6.2.3. Volume of a Cube Cuboid and Cylinder  6.2.4. Volume of a Cone and Sphere  6.3. Conversion of Units  6.4. Frustum of a Cone
  7. Statistics  7.1. Introduction to Statistics  7.2. Collection of Data  7.3. Presentation of Data  7.3.1. Tabular Form  7.3.2. Graphical Form  7.3.2.1. Bar Graph  7.3.2.2. Histogram  7.3.2.3. Frequency Polygon  7.3.2.4. Ogive  7.4. Measures of Central Tendency  7.4.1. Mean Median and Mode  7.4.2. Quartiles and Percentiles  7.5. Measures of Dispersion  7.5.1. Range and Interquartile Range  7.5.2. Standard Deviation and Variance
  8. Probability  8.1. Introduction to Probability  8.2. Experimental Probability  8.3. Theoretical Probability  8.4. Probability of Simple Events  8.5. Complementary Events  8.6. Probability of Compound Events

Grade 10 → Statistics → Presentation of Data → Graphical Form ↓


Frequency Polygon


A frequency polygon is a graphical representation of the distribution of a dataset. It is used to show the frequencies of different classes, intervals, or categories within a dataset. A frequency polygon is constructed by drawing a line graph of connected frequencies, which can be interpreted in a similar way to a histogram.

Understanding frequency polygons

At the core of the frequency polygon are the terms "frequency" and "class interval." Let's break down these concepts to better understand the purpose and construction of the frequency polygon.

Frequency

Frequency refers to the number of times a particular value or range of values appears in a dataset. For example, if we are analyzing students' scores on a test, a score of 80 might have a frequency of 5, indicating that five students scored 80 marks.

Class interval

In many cases, especially with continuous data, individual values are grouped into class intervals. A class interval is a range of values over which we want to measure frequency. For example, when looking at the age of people in a community, the class intervals might be 10-19, 20-29, 30-39, and so on.

Construction of frequency polygon

Follow these general steps to construct a frequency polygon:

  1. Create a frequency distribution table: Summarize the data in terms of classes and their corresponding frequencies.
  2. Determine the class midpoint: Calculate the midpoint of each class interval. This is done by taking the average of the upper and lower limits of each class interval.
  3. Plot the midpoints and frequencies: Make a graph with the midpoints on the horizontal axis (x-axis) and the frequencies on the vertical axis (y-axis).
  4. Connect the dots: Plot the points corresponding to each midpoint and its frequency, then connect these points with straight lines.
  5. Close the polygon: To completely construct the polygon, extend the lines back to the horizontal axis at the midpoint before the first square and after the last square.

Example of constructing a frequency polygon

Let us consider the following frequency distribution for the age of participants in a study:

Group (Age) Frequency
10-19        5
20-29       15
30-39       25
40-49       30
50-59       20
60-69       10

Step 1: Determine the orbit midpoint

The midpoint of a class can be found by adding the lower and upper class limits and dividing by 2.

10-19: (10 + 19) / 2 = 14.5
20-29: (20 + 29) / 2 = 24.5
30-39: (30 + 39) / 2 = 34.5
40-49: (40 + 49) / 2 = 44.5
50-59: (50 + 59) / 2 = 54.5
60-69: (60 + 69) / 2 = 64.5

Step 2: Plot the points

For each class midpoint, plot a point on the graph aligning the midpoint with its frequency.

0 14.5 24.5 34.5 44.5 54.5 64.5 5 15 25 35

Step 3: Generate the frequency polygon

By connecting the plotted points, we create a frequency polygon, which effectively allows us to visualize the distribution of the data. The start and end points of the line extend to the x-axis, similar to a typical polygon shape.

Applications of frequency polygon

Frequency polygons are useful in various aspects of data analysis. Some of their applications are as follows:

  • Comparative analysis: By overlaying frequency polygons, different data sets can be compared and differences in their distributions can be observed.
  • Data summary: Provide a clear picture of the dataset in graphical form, and also help visualize central tendency and variability.
  • Finding patterns and trends: Helps identify correlations, patterns, or trends in data.

Conclusion

Frequency polygons are a simple but powerful tool for visualizing the distribution of frequency data. They provide clarity in seeing how data is distributed and can be effectively used to compare datasets. Understanding frequency polygons and their proper construction is an essential skill in statistics.


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Frequency Polygon

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