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
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 (less than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84 | 105 | 147 | 180 | 196 | 200 |
Draw an ogive for the following :
| Age in years | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |
| No. of people | 0 | 17 | 42 | 67 | 100 |
The weight of 50 workers is given below:
| Weight in Kg | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 |
| No. of Workers | 4 | 7 | 11 | 14 | 6 | 5 | 3 |
Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:
1) The upper and lower quartiles.
2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.
Draw a cumulative frequency curve (ogive) for the following distributions:
| Class Interval | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
| Frequency | 10 | 15 | 17 | 12 | 10 | 8 |
Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:
| Weight (gms) | Frequency |
| 50 - 60 | 8 |
| 60 - 70 | 10 |
| 70 - 80 | 12 |
| 80 - 90 | 16 |
| 90 - 100 | 18 |
| 100 - 110 | 14 |
| 110 - 120 | 12 |
| 120 - 130 | 10 |
(i) Calculate the cumulative frequencies.
(ii) Draw the cumulative frequency curve and form it determine the median weights of the potatoes.
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 |
Draw an ogive for the following distributions:
| Age in years (less than) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| Cumulative frequency | 0 | 17 | 32 | 37 | 53 | 58 | 65 |
