Topics
Commercial Mathematics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Goods and Services Tax (G.S.T.)
Algebra
Banking
Geometry
Shares and Dividends
Linear Inequations
Mensuration
Quadratic Equations
Trigonometry
Ratio and Proportion
Statistics
Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Probability
Matrices
Arithmetic and Geometric Progression
Co-ordinate Geometry
- Foundation of Coordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Similarity
Symmetry
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Circles
Tangent and Secant Properties
Constructions
Area and Volume of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
Probability
Key Points: Frequency Polygon
-
A frequency polygon is a graph obtained by joining the points
(class-mark, frequency) by straight line segments. -
Class-mark = midpoint of the class interval.
-
Two imagined classes (with zero frequency) are taken at the beginning and end to close the polygon.
-
A frequency polygon is drawn on the same axes as the histogram (if a histogram is given).
-
The polygon starts and ends on the x-axis.
Related QuestionsVIEW ALL [11]
In a study of dental problem, the following data were obtained.
| Ages | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 | 50 − 60 | 60 − 70 | 70 − 80 |
| No. of patients | 5 | 13 | 25 | 14 | 30 | 35 | 43 | 50 |
Represent the above data by a frequency polygon.
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 |
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 |
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 |
The distribution of heights (in cm) of 100 people is given below. Construct a histogram and the frequency polygon imposed on it.
| Height (in cm) |
125 − 135 | 136 − 146 | 147 − 157 | 158 − 168 | 169 − 179 | 180 − 190 | 191 − 201 |
| Frequency | 12 | 22 | 18 | 24 | 15 | 7 | 2 |
