Topics
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
Commercial Mathematics
Goods and Services Tax (G.S.T.)
Banking
Algebra
Geometry
Shares and Dividends
Mensuration
Symmetry
Linear Inequations
Trigonometry
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Statistics
Problems on Quadratic Equations
- Method for Solving a Quadratic Word Problem
- Problems Based on Numbers
- Problems on Ages
- Problems Based on Time and Work
- Problems Based on Distance, Speed and Time
- Problems Based on Geometrical Figures
- Problems on Mensuration
- Problems on C.P. and S.P.
- Miscellaneous Problems
Probability
Ratio and Proportion
Remainder Theorem and Factor Theorem
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic Progression
Geometric Progression
Reflection
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Section and Mid-Point Formulae
Equation of a Line
- Equations of Line in Different Forms
- Inclination of a Line
- Concept of Slope (or, gradient)
- Intercepts on Axes
- Equally Inclined lines
- Problems Based on Slope and Y-Intercept
Similarity
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
Angle and Cyclic Properties of a Circle
Tangent Properties of Circles
Constructions
Volume and Surface Area 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
Graphical Representation of Statistical Data
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
Definition: Ogive (Cumulative Frequency Curve)
An ogive is a freehand curve obtained by plotting upper class limits on the x-axis and their corresponding cumulative frequencies on the y-axis.
Key Points: Ogive (Cumulative Frequency Curve)
-
Ogive is also called a cumulative frequency curve.
-
The ogive is also called the less-than ogive.
-
It is always a rising curve.
-
It starts at the lower limit of the first class with a cumulative frequency of 0.
-
It ends at the upper limit of the last class.
-
Ogive is drawn only after converting inclusive classes into an exclusive form.
Video Tutorials
Shaalaa.com | Statistics part 14 (Graphical Representation Cumulative Frequency)
Related QuestionsVIEW ALL [30]
Construct a frequency distribution table for the following distributions:
| Marks (more than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative frequency | 100 | 87 | 65 | 55 | 42 | 36 | 31 | 21 | 18 | 7 | 0 |
Draw an ogive by less than method for the following data:
| No. of rooms: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of houses: | 4 | 9 | 22 | 28 | 24 | 12 | 8 | 6 | 5 | 2 |
Prepare the cumulative frequency (less than types) table from the following distribution table :
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 2 | 3 | 7 | 8 | 5 |
Draw an ogive for the following :
| Marks (More than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative Frequency | 100 | 87 | 65 | 55 | 42 | 36 | 31 | 21 | 18 | 7 | 0 |
The following table gives production yield per hectare of wheat of 100 farms of a village:
| Production yield in kg per hectare: | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |
| Number of farms: | 2 | 8 | 12 | 24 | 38 | 16 |
Draw ‘less than’ ogive and ‘more than’ ogive.
Draw an ogive for the following:
| Marks obtained | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |
| No. of students | 8 | 22 | 48 | 60 | 75 |
Draw an ogive for the following :
| Marks obtained | More than 10 | More than 20 | More than 30 | More than 40 | More than 50 |
| No. of students | 8 | 25 | 38 | 50 | 67 |
Draw an ogive for the following distributions:
| Marks obtained | less than 10 | less than 20 | less than 30 | less than 40 | less than 50 |
| No. of students | 8 | 25 | 38 | 50 | 67 |
