Topics
Linear equations in two variables
- Linear Equations in Two Variables
- Linear Equations in Two Variables Applications
- Cross - Multiplication Method
- Substitution Method
- Elimination Method
- Graphical Method of Solution of a Pair of Linear Equations
- Determinant of Order Two
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Simple Situational Problems
- Inconsistency of Pair of Linear Equations
- Cramer'S Rule
- Consistency of Pair of Linear Equations
- Pair of Linear Equations in Two Variables
Quadratic Equations
- Quadratic Equations Examples and Solutions
- Quadratic Equations
- Roots of a Quadratic Equation
- Nature of Roots
- Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Formula for Solving a Quadratic Equation
Arithmetic Progression
- Introduction to Sequence
- Geometric Mean
- Arithmetic Progressions Examples and Solutions
- Arithmetic Progression
- Geometric Progression
- General Term of an Arithmetic Progression
- General Term of an Geomatric Progression
- Sum of First n Terms of an AP
- Sum of the First 'N' Terms of an Geometric Progression
- Arithmetic Mean - Raw Data
- Terms in a sequence
- Concept of Ratio
Financial Planning
Probability
- Basic Ideas of Probability
- Probability - A Theoretical Approach
- Type of Event - Elementry
- Type of Event - Complementry
- Type of Event - Exclusive
- Type of Event - Exhaustive
- Equally Likely Outcomes
- Probability of an Event
- Concept Or Properties of Probability
- Addition Theorem
- Random Experiments
- Sample Space
- Basic Ideas of Probability
Statistics
- Tabulation of Data
- Inclusive and Exclusive Type of Tables
- Median of Grouped Data
- Mean of Grouped Data
- Graphical Representation of Data as Histograms
- Frequency Polygon
- Concept of Pie Graph (Or a Circle-graph)
- Concept of Pie Graph (Or a Circle-graph)
- 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
- Graphical Representation of Data as Histograms
- Mode of Grouped Data
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 [7]
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) | 85-100 | 100-115 | 115-130 | 130-145 |
| 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 |
