
1.Number System
14
Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

Lecture1.7

Lecture1.8

Lecture1.9

Lecture1.10

Lecture1.11

Lecture1.12

Lecture1.13

Lecture1.14


2.Polynomials
10
Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Lecture2.5

Lecture2.6

Lecture2.7

Lecture2.8

Lecture2.9

Lecture2.10


3.Coordinate Geometry
8
Lecture3.1

Lecture3.2

Lecture3.3

Lecture3.4

Lecture3.5

Lecture3.6

Lecture3.7

Lecture3.8


4.Linear Equations
8
Lecture4.1

Lecture4.2

Lecture4.3

Lecture4.4

Lecture4.5

Lecture4.6

Lecture4.7

Lecture4.8


5.Euclid's Geometry
7
Lecture5.1

Lecture5.2

Lecture5.3

Lecture5.4

Lecture5.5

Lecture5.6

Lecture5.7


6.Lines and Angles
10
Lecture6.1

Lecture6.2

Lecture6.3

Lecture6.4

Lecture6.5

Lecture6.6

Lecture6.7

Lecture6.8

Lecture6.9

Lecture6.10


7.Triangles
11
Lecture7.1

Lecture7.2

Lecture7.3

Lecture7.4

Lecture7.5

Lecture7.6

Lecture7.7

Lecture7.8

Lecture7.9

Lecture7.10

Lecture7.11


8.Quadrilaterals
13
Lecture8.1

Lecture8.2

Lecture8.3

Lecture8.4

Lecture8.5

Lecture8.6

Lecture8.7

Lecture8.8

Lecture8.9

Lecture8.10

Lecture8.11

Lecture8.12

Lecture8.13


9.Area of Parallelogram
11
Lecture9.1

Lecture9.2

Lecture9.3

Lecture9.4

Lecture9.5

Lecture9.6

Lecture9.7

Lecture9.8

Lecture9.9

Lecture9.10

Lecture9.11


10.Constructions
7
Lecture10.1

Lecture10.2

Lecture10.3

Lecture10.4

Lecture10.5

Lecture10.6

Lecture10.7


11.Circles
11
Lecture11.1

Lecture11.2

Lecture11.3

Lecture11.4

Lecture11.5

Lecture11.6

Lecture11.7

Lecture11.8

Lecture11.9

Lecture11.10

Lecture11.11


12.Heron's Formula
8
Lecture12.1

Lecture12.2

Lecture12.3

Lecture12.4

Lecture12.5

Lecture12.6

Lecture12.7

Lecture12.8


13.Surface Area and Volume
16
Lecture13.1

Lecture13.2

Lecture13.3

Lecture13.4

Lecture13.5

Lecture13.6

Lecture13.7

Lecture13.8

Lecture13.9

Lecture13.10

Lecture13.11

Lecture13.12

Lecture13.13

Lecture13.14

Lecture13.15

Lecture13.16


14.Statistics
15
Lecture14.1

Lecture14.2

Lecture14.3

Lecture14.4

Lecture14.5

Lecture14.6

Lecture14.7

Lecture14.8

Lecture14.9

Lecture14.10

Lecture14.11

Lecture14.12

Lecture14.13

Lecture14.14

Lecture14.15


15.Probability
8
Lecture15.1

Lecture15.2

Lecture15.3

Lecture15.4

Lecture15.5

Lecture15.6

Lecture15.7

Lecture15.8

Chapter Notes – Statistics – Graphical Representation of Statistical Data
(1) Following are the methods of graphical representation of data:
(i) Bar graphs:
For Example: The population of Delhi state in different census years is as given below:Represent the above information with the help of a bar graph.
Solution: To represent the given data by a pictograph follow the below steps:
Step 1: Draw a horizontal and vertical line.
Step 2: Mark 5 point on horizontal line at equal distance for census year.
Step 3: Erect rectangles of the same width at marked points.
Step 4: The height of the rectangles are proportional to the numerical values of the given population.
(ii) Histogram:
For Example: Construct a histogram for the following data:Solution: To represent the given data by a histogram follow the below steps:
Step 1: Draw a horizontal and vertical line.
Step 2: Taking class interval on horizontal line and corresponding frequencies on vertical line.
Step 3: Construct rectangles to obtain the histogram of given frequency distribution as shown in fig.
(iii) Frequency polygon:
For Example: The following table gives the distribution of IQ’s (intelligence quotients) of 60 pupils of class V in a school:Draw a frequency polygon for the above data.
Solution: To represent the given data by frequency polygon follow the below steps:
Step 1: We need to find class mark.
We know, Class Mark = (Upper limit + Lower limit)/2.
Expenditure  Class Mark  No. of workers 
62.5 – 69.5  66  1 
69.5 – 76.5  73  3 
76.5 – 83.5  80  5 
83.5 – 90.5  87  15 
90.5 – 97.5  94  12 
97.5 – 104.5  101  10 
104.5 – 111.5  108  6 
111.5 – 118.5  115  4 
118.5 – 125.5  122  3 
125.5 – 132.5  129  1 
Step 2: Draw a horizontal and vertical line.
Step 3: Taking class interval on horizontal line and corresponding frequencies on vertical line.
Step 4: Plot (66, 1), (73, 3), (80, 5), (87, 15), (94, 12), (101, 10), (108, 6), (115, 4), (122, 3), (129, 1)
Step 5: Join the plotted points.
Step 6: The end point (66, 1) and (129, 1) are joined to the midpoint (59, 0) and (136, 0) respectively of imagined class intervals to obtain the frequency polygon.
(2) A bar graph is a pictorial representation of the numerical data by a number of bars (rectangles) of uniform width erected horizontally or vertically with equal spacing between them. Each rectangle or bar represents only one value of the numerical data and so there are as many bars as the number of values in the numerical data. The height or length of a bar indicates on a suitable scale the corresponding value of the numerical data.
For Example: The following table shows the daily production of T.V. sets in an industry for 7 days of a week:Represent the above information by a pictograph.
Solution: To represent the given data by a pictograph follow the below steps:
Step 1: Draw a horizontal and vertical line.
Step 2: Mark 7 days on horizontal line at equal distance.
Step 3: Erect rectangles of the same width at marked points.
Step 4: The height of the rectangles are proportional to the numerical values of the given data of no of TV sets.
(3) A histogram or frequency histogram is a graphical representation of a frequency distribution in the form of rectangles with class intervals as bases and heights proportional to corresponding frequencies such that there is no gap between any two successive rectangles.
For Example: Construct a histogram for the following data:Solution: To represent the given data by a histogram follow the below steps:
Step 1: Draw a horizontal and vertical line.
Step 2: Taking class interval on horizontal line and corresponding frequencies on vertical line.
Step 3: Construct rectangles to obtain the histogram of given frequency distribution as shown in fig.
(4)A frequency polygon of a given frequency distribution is another method of representing frequency distribution graphically.
For Example: Draw, in the same diagram, a histogram and a frequency polygon to represent the following data which shows the monthly cost of living index of a city in a period of 2 years:Solution: To represent the given data by a histogram follow the below steps:
Step 1: Draw a horizontal and vertical line.
Step 2: Taking class interval on horizontal line and corresponding frequencies on vertical line.
Step 3: Construct rectangles to obtain the histogram of given frequency distribution as shown in fig.
Step 4: Obtain the midpoints of the upper horizontal side of each rectangle.
Step 5: Join these midpoints of the adjacent rectangles of the histogram by line segment.
Step 6: Obtain the midpoints of two class intervals of zero frequency i.e. on X axis, one adjacent to the first, on its left and one adjacent to the last, on its right.
These class intervals are known as imagined class intervals.
Step 7: Complete the polygon by joining the midpoints of first and last intervals to the midpoints of imagined class interval adjacent to them.