Topics
Linear equations in two variables
 Linear Equation in Two Variables
 Simultaneous Linear Equations
 Elimination Method
 Substitution Method
 Cross  Multiplication Method
 Graphical Method of Solution of a Pair of Linear Equations
 Determinant of Order Two
 Cramer’s Rule
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Simple Situational Problems
 Pair of Linear Equations in Two Variables
Quadratic Equations
 Quadratic Equations
 Roots of a Quadratic Equation
 Solutions of Quadratic Equations by Factorization
 Solutions of Quadratic Equations by Completing the Square
 Formula for Solving a Quadratic Equation
 Nature of Roots of a Quadratic Equation
 The Relation Between Roots of the Quadratic Equation and Coefficients
 To Obtain a Quadratic Equation Having Given Roots
 Application of Quadratic Equation
Arithmetic Progression
 Introduction to Sequence
 Terms in a sequence
 Arithmetic Progression
 General Term of an Arithmetic Progression
 Sum of First n Terms of an A.P.
 Arithmetic Progressions Examples and Solutions
 Geometric Progression
 General Term of an Geomatric Progression
 Sum of the First 'N' Terms of an Geometric Progression
 Geometric Mean
 Arithmetic Mean  Raw Data
 Concept of Ratio
Financial Planning
Probability
 Probability  A Theoretical Approach
 Basic Ideas of Probability
 Random Experiments
 Outcome
 Equally Likely Outcomes
 Sample Space
 Event and Its Types
 Probability of an Event
 Type of Event  Elementry
 Type of Event  Complementry
 Type of Event  Exclusive
 Type of Event  Exhaustive
 Concept Or Properties of Probability
 Addition Theorem
Statistics
 Tabulation of Data
 Inclusive and Exclusive Type of Tables
 Ogives (Cumulative Frequency Graphs)
 Applications of Ogives in Determination of Median
 Relation Between Measures of Central Tendency
 Introduction to Normal Distribution
 Properties of Normal Distribution
 Concepts of Statistics
 Mean of Grouped Data
 Method of Finding Mean for Grouped Data: Direct Method
 Method of Finding Mean for Grouped Data: Deviation Or Assumed Mean Method
 Method of Finding Mean for Grouped Data: the Step Deviation Method
 Median of Grouped Data
 Mode of Grouped Data
 Concept of Pictograph
 Presentation of Data
 Graphical Representation of Data as Histograms
 Frequency Polygon
 Concept of Pie Graph (Or a Circlegraph)
 Interpretation of Pie Diagram
 Drawing a Pie Graph
Notes
The information in a frequency table can be presented in various ways. We have studied a histogram. A frequency polygon is another way of presentation.
Let us study two methods of drawing a frequency polygon.
(1) With the help of a histogram (2) Without the help of a histogram.
(1) We shall use the histogram in figure to learn the method of drawing a frequency polygon.
1. Mark the mid  point of upper side of each rectangle in the histogram.
2. Assume that a rectangle of zero height exists preceeding the first rectangle and mark its mid  point. Similarly, assume a rectangle succeeding the last rectangle and mark its mid point.
3. Join all mid  points in order by line segments.
4. The closed figure so obtained is the frequency polygon.
(2) Observe the following table. It shows how the coordinates of points are decided to draw a frequency polygon, without drawing a histogram.
The points corresponding to the coordinates in the fifth column are plotted. Joining them in order by line segments, we get a frequency polygon. The polygon is shown in figure . Observe it.
Related QuestionsVIEW ALL [8]
Draw a frequency polygon from the information given in the following table.
Age of blood donar (Years)  No. of blood donars 
Less than 20  0 
Less than 25  30 
75Less than 30  75 
165Less than 35  127 
Less than 40  165 
Less than 45  185 
Less than 50  197 
In a handloom factory different workers take different periods of time to weave a saree. The number of workers and their required periods are given below. Present the information by a frequency polygon.
No. of days

8  10  10  12  12  14  14  16  16  18  18  20 
No. of workers  5  16  30  40  35  14 
The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon.
Time required for
experiment (minutes) 
20  22  22  24  24  26  26  28  28  30  30  32 
No. of students  8  16  22  18  14  12 
Draw a frequency polygon for the following grouped frequency distribution table.
Age of the donor
(Yrs.) 
20  24  25  29  30  34  35  39  40  44  45  49 
No. of blood doners  38  46  35  24  15  12 
The following table shows the average rainfall in 150 towns. Show the information by a frequency polygon.
Average rainfall (cm)

0  20  20  40  40  60  60  80  80  100 
No. of towns  14  12  36  48  40 
The maximum bowing speed (km/hour) or 33 players at a cricket coaching centre is given below:
Bowling Speed(km/hour)  85100  100115  115130  130145 
Numbers of players  9  11  8  5 
find the modal bowling speed of players.
The time required for some students to complete a science experiment and the number of students is shown in the following grouped frequency distribution table. Draw the frequency polygon with the help of histogram using given information:
Time required for experiment (minutes)  Number of Students 
20  22  6 
22  24  14 
24  26  20 
26  28  16 
28  30  12 
30  32  10 
In the following frequency distribution, the heights of 90 students are recorded and the frequency polygon is drawn.
Heights  30 – 35  35 – 40  40 – 45  45 – 50  50 – 55  55 – 60 
No. of Students  6  12  20  18  24  10 