Histograms

Topics

Goods and Services Tax (G.S.T.)
- Tax and Its Computation
- Mathematical Study of GST (Goods and Services Tax)
- GST Structure for Calculations
- Computational Mechanisms under GST
- Input Tax Credit (ITC) in Mathematics
- E-way Bill in GST Sums
- Examples based on GST Calculations
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
Banking
- Money and Banking in Arithmetic
- Mathematics of Recurring Deposit (R.D.)
Algebra
Shares and Dividends
- Shares
- Formulae for Shares and Dividends
- Examples based on Shares and Dividends
Geometry
Mensuration
Linear Inequations
- Linear Inequations
- Method of Solving a Linear Inequality
- Representation of Inequalities
- Combining Inequalities
- Product of Two Linear Expressions
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
Ratio and Proportion
- Ratio
- Ratio in Lowest Terms
- All About Ratios: Dividing, Comparing, and Modifying Quantities
- Commensurable and Incommensurable Quantities
- Composition of Ratios
- Proportion
- Concept of Continued Proportion
- Properties of Proportion
- Direct Applications of Ratio and Proportion
Probability
Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
- Concept of Matrices
- Types of Matrices
- Equality of Matrices
- Compatibility of Matrices
- Transpose of a Matrix
- Operations on Matrices> Addition and Subtraction of Matrices
- Operations on Matrices> Matrix Multiplication
- Operations on Matrices>Scalar Multiplication
Arithmetic and Geometric Progression
- Sequence, Series, and Progression
- Arithmetic Progression (A.P.)
- General Term of an Arithmetic Progression
- Sum of First ‘n’ Terms of an Arithmetic Progressions
- Three or More Terms in Arithmetic Progression (A.P.)
- Arithmetic Mean in A.P.
- Properties of an Arithmetic Progression
Co-ordinate Geometry
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Symmetry
Similarity
- Similarity and Congruency of Figures
- Similarity as a Size Transformation
- Applications to Maps and Models
- Similarity of Triangles (Corresponding Sides & Angles)
- Criteria for Similarity of Triangles
- Basic Proportionality Theorem
- Relation Between the Areas of Two Triangles
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
- Geometrical Concepts Related to a Circle
- Chord
- Arc of the Circle
- Segment of a Circle
- Theorems on Angles in a Circle
- Cyclic Quadrilateral and Concyclic Points
- Some Important Results on Circles
- Advanced Theorems Related to Circles
Tangent and Secant Properties
- Secant and Tangent
- Tangent and Secant Properties
- Intersecting Chords and Tangents
- Alternate Segment Property
Constructions
- Construction of Tangents to a Circle
- Construction of Two Tangents to a Circle
- Circumcircle of a Triangle
- Incircle of a Triangle
- Circumscribed Circle of a Regular Polygon
- Inscribed Circle of a Regular Polygon
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
- Trigonometric Ratios
- Relation Among Trigonometric Ratios
- Trigonometric Identities (Square Relations)
- Elimination of Trigonometrical Ratios
- Trigonometric Ratios of Complementary Angles
- Application of Trigonometric Tables
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
- Frequency Distribution and Its Applications
- Concepts of Statistics
- Histograms
- Frequency Polygon
- Cumulative Frequency and Cumulative Frequency Table
- Ogives (Cumulative Frequency Curve)
Probability
- Concept of Probability
- Elementary Types of Events and Properties of Probability
- Measurement of Probability
- Standard Results for Outcomes in Probability
- Problems based on Probability

Maharashtra State Board: Class 10
CISCE: Class 10

Key Points: Histograms

A Histogram is a graphical representation of a grouped frequency distribution using rectangles.
It is used for continuous grouped data.
Class intervals are shown on the X-axis.
Frequencies are shown on the Y-axis.
Rectangles are drawn without gaps between them.
The height of each rectangle is proportional to its frequency.

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Concept of Histrogram [00:13:21]

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The top speeds of thirty different land animals have been organised into a frequency table. Draw a histogram for the given data.

Maximum Speed (km/h)	Frequency
10 – 20	5
20 – 30	5
30 – 40	10
40 – 50	8
50 – 60	0
60 – 70	2

Draw a histogram for the daily earnings of 30 drug stores in the following table:

Daily earnings (in Rs):	450−500	500−550	550−600	600−650	650−700
Numbers of stores:	16	10	7	3	1

The weekly wages (in Rs.) of 30 workers in a factory are given:
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:
(i) Which group has the maximum number of workers?
(ii) How many workers earn Rs 850 and more?
(iii) How many workers earn less than Rs 850?

In a village, there are 570 people who have cell phones. An NGO survey their cell phone usage. Based on this survey a histogram is drawn

Are people using cell phone for less than 1 hour?

Draw histogram and frequency polygon on the same graph paper for the following frequency distribution

Class	Frequency
15-20	20
20-25	30
25-30	50
30-35	40
35-40	25
40-45	10

The following is the frequency distribution of waiting time at ATM centre; draw histogram to represent the data:

Waiting time (in seconds)	Number of Customers
0 -30	15
30 - 60	23
60 - 90	64
90 - 120	50
120 - 150	5

The following histogram shows the number of literate females in the age group of 10 to 40 years in a town:

(i) Write the age group in which the number of literate female is the highest.
(ii) What is the class width?
(iii) What is the lowest frequency?
(iv) What are the class marks of the classes?
(v) In which age group literate females are the least?

The following histogram shows the frequency distribution f the ages of 22 teachers in a school:

(i) What is the number of eldest and youngest teachers in the school?
(ii) Which age group teachers are more in the school and which least?
(iii) What is the size of the classes?
(iv) What are the class marks of the classes?

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Topics

Goods and Services Tax (G.S.T.)

Commercial Mathematics

Compound Interest

Banking

Algebra

Shares and Dividends

Geometry

Mensuration

Linear Inequations

Trigonometry

Quadratic Equations

Statistics

Ratio and Proportion

Probability

Factorisation of Polynomials

Matrices

Arithmetic and Geometric Progression

Co-ordinate Geometry

Symmetry

Similarity

Loci

Circles

Tangent and Secant Properties

Constructions

Area and Volume of Solids (Cylinder, Cone and Sphere)

Trigonometrical Identities

Heights and Distances

Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive

Probability

Key Points: Histograms

Shaalaa.com | Concept of Histrogram

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Series: Graphical Representation of Data as Histograms

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