On the other hand, frequency polygon is an approximate curve, but still it is more usefui as compared to histogram. Therefore, the modified tables are: We plot the ordered pairs (5, 3), (15, 9), (25, 17), (35, 12) and (45, 9) and join the points by line segments and obtain the frequency polygon of section A. To find the class-mark of a class interval, we find the sum of the upper limit and lower limit of a class and divide it by 2. 14.5.2. To create a frequency polygon, start just as for histograms, by choosing a class interval. Solution : Note that the variable here is the ‘month of birth’, and the value of the variable is the ‘Number of students born’. Frequency polygons are analogous to line graphs, and just as line graphs make continuous data visually easy to interpret, so too do frequency polygons. To complete the polygon, we assume that there is a class interval with frequency zero The midpoint values are shown along the horizontal axis, and the frequency values are shown along the vertical axis like for a histogram: The values of the variable are shown on the other axis (say, the y-axis) and the heights of the bars depend on the values of the variable. For instance, the frequency for the midpoint value 8 is 5. In the example above, the minimum class-size is 10. Online Tests . In a city, the weekly observations made in a study on the cost of living index are given in the following table: Draw a frequency polygon for the data above (without constructing a histogram). Why Frequency polygons are analogous to line graphs, and just as line graphs make continuous data visually easy to interpret, so too do frequency polygons. Let us call these mid-points B, C, D, E, F and G. When joined by line segments, we obtain the figure BCDEFG (see Fig. 14.3. Ø Then these points are then joined by a straight line. Now, if you instead need to graph a cumulative frequency polygon, you will need instead this ogive graph maker. It is very useful for comparing two different sets of data of the same nature, for example, comparing the performance of two different sections of the same class. The RS Aggarwal Solutions for Class 9 Chapter-17 Bar Graph, Histogram and Frequency Polygon Maths have been provided here for the benefit of the CBSE Class 9 students. 8-9 b. Frequency Polygons when the Frequency Distribution is Exclusive. Since the maximum frequency is 15, we need to choose the scale to accomodate this maximum frequency. Then she formed the following table: Carefully examine this graphical representation. Frequency polygons are analogous to line graphs, and just as line graphs make continuous data visually easy to interpret, so too do frequency polygons. Observe the bar graph given above and answer the following questions: For instance, when the class-size is 20, the length of the rectangle is 7. Videos, worksheets, 5-a-day and much more Frequency Polygons. Frequency Polygons; Class 9 NCERT (CBSE and ICSE) Frequency Polygons. 14.6). Solution: In Fig. Usually comparisons among the individual items are best shown by means of graphs. However, since the widths of the rectangles are all equal, the lengths of the rectangles are proportional to the frequencies. A frequency polygon is a line graph that connects the midpoints of each class interval at the top end of each rectangle in a histogram. To see what we mean, consider the histogram represented by Fig. ., 60 - 70, 70 - 100. A frequency polygon can be drawn from a (a) Histogram, (b) Frequency table 3. The representation then becomes easier to understand than the actual data. Frequency Polygon. Frequency polygons are used when the data is continuous and very large. The exercise contains a total of 9 questions. What are the boundaries for 8.6-8.8? The first class is zero days with zero frequency. Let L be the mid-point of the class succeeding the last class of the given data. before 30.5 - 35.5, and one after 55.5 - 60.5, and their mid-points are A and H, respectively. These mid-points of the class-intervals are called class-marks. (b) Without using Histogram: Steps: Find the class-mark (mid-value) of each given class-interval. Online Practice . Solution : Let us first draw a histogram for this data and mark the mid-points of the tops of the rectangles as B, C, D, E, F, G, H, I, J, K, respectively. Time (t minutes) Frequency 0 < t 10 4 10 < t 20 8 20 < t 30 14 30 < t 40 16 40 < t 50 6 50 < t 60 2 (a) Draw a frequency polygon for this information. For instance, consider the frequency distribution Table 14.6, representing the weights of 36 students of a class: Let us represent the data given above graphically as follows: Observe that since there are no gaps in between consecutive rectangles, the resultant graph appears like a solid figure. A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Ø The Frequency Polygon is a curve representing a frequency distribution. All Chapter-17 Bar Graph, Histogram and Frequency Polygon Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks in your final exams. Thus.                           (i) How many students were born in the month of November? But if only frequency polygon is to be drawn then first represent the class marks along x-axis and frequencies along y-axis and then plot the point corresponding to the frequency at each class mark. There is yet another visual way of representing quantitative data and its frequencies. So say we have the frequency table from the earlier example: Now what were going to do is plot a graph showing the frequency for each midpoint. Example 2: Construct a frequency polygon for the following data : Solution: First we obtain the class marks as given in the following table. A student collects information about the number of school going children in a locality consisting of a hundred households. Example 8 : Consider the marks, out of 100, obtained by 51 students of a class in a test, given in Table 14.9. Ø In frequency polygon, the mid values of each class are first obtained. Rs Aggarwal 2018 Solutions for Class 9 Math Chapter 17 Bar Graph, Histogram And Frequency Polygon are provided here with simple step-by-step explanations. Although, there exists no class preceding the lowest class and no class succeeding the highest class, addition of the two class intervals with zero frequency enables us to make the area of the frequency polygon the same as the area of the histogram. The midpoint of a class is the point in the middle of the class. (ii) We represent the number of students (frequency) on the vertical axis on a suitable scale. Also, make frequency polygon. (ii) In which month were the maximum number of students born? 14.8). Draw the Y-axis to indicate the frequency of each class. ... Bar Graph. Overlaid Frequency Polygon: Also to compare the distributions of different data sets, frequency polygon can be used. Continuing in the same manner, we find the class-marks of the other classes as well. The graph is the same as before except that the Y value for each point is the number of students in the corresponding class interval plus all numbers in lower intervals. Represent Rational Numbers on the Number Line, Find Rational Numbers Between Given Rational Numbers, Without Actual Division Identify Terminating Decimals, Express Rational Numbers as Terminating and Recurring Decimals, Express Terminating Decimals as Fractions, Represent Irrational Numbers on the Number Line, Find Irrational Numbers Between Given Rational Numbers, Multiplication and Division of Real Numbers, Real Numbers: Mixed Operations (Simplification), Simplify and Find Values of Expressions using Rationalization, Simplify Expressions Using the Laws of Radicals, Factorization by Taking out the Common Factor, Factorization Using the Identity for Square of a Trinomial, Factorization of Sum or Difference of Cubes, Evaluate Polynomials Using Algebraic Identities, Understand the Terms Related to Coordinate Geometry, Identify the Coordinates of a Point on the Cartesian Plane, Identify the Coordinates of the Points on the X-axis, Y-axis, and the Origin, Higher Order Thinking Skills (HOTS) Related to the Cartesian Plane, Verify a Solution to a Linear Equation in Two Variables, Find the Unknown Variable When the Equation of the Line and Several Conditions are Given, Draw Graph of Linear Equations and Find the Unknown Variable, Draw Graph of Some Special Type of Linear Equations, Understanding Points, Line Segments, Rays, Lines, and Planes, Parallel, Concurrent and Intersecting Lines, Understand the Concept of Angles and Terms Related to Angles, Categorize Angles on the Basis of Their Measures, Complementary and Supplementary Pairs of Angles, Adjacent Angles, Vertically Opposite Angles, and Linear Pair of Angles, Parallel Lines, Transversal, and Angles Formed, Classification of Triangles on the Basis of its Sides and Angles, Theorems and Problems Related to Side and Angle Measures of Triangles, Problems Related to Congruence of Triangles, Understand the Concept of Quadrilaterals and Related Terms, Theorems and Problems Related to the Angles of a Quadrilateral, Theorems and Problems Related to Parallelograms, Intercept Theorem (Thales Theorem, or Basic Proportionality Theorem) and Related Problems, Theorems and Problems Related to Chord Properties of Circles, Theorems and Problems Related to Angles Subtended by Arcs/Chords, Theorems and Problems Related to Cyclic Quadrilaterals, Problems Related to Circumcircles and In-circles, Volume and Surface Area of Cuboids and Cubes, Volume and Surface Area of Circular Cones, Volume and Surface Area of Spheres, Hemispheres and Spherical Shells, Mixed Problems on Volume and Surface Area, Frequency Distribution of an Ungrouped Data, Cumulative Frequency Table of an Ungrouped Data, Histogram When the Frequency Distribution is Exclusive, Histogram When the Frequency Distribution is Inclusive, Histogram When the Class Intervals are of Unequal Size, Frequency Polygons when the Frequency Distribution is Exclusive, Frequency Polygons when the Frequency Distribution is Inclusive, Histograms and Frequency Polygons on a Single Graph, Calculate Probability for Events in Random Experiments, Area of a Quadrilateral Using Heron's Formula, Application of Results on Area of Polygonal Regions. 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