## Data Handling Class 7 Notes Maths Chapter 3

CBSE Class 7 Maths Notes Chapter 3 Data Handling Pdf free download is part of Class 7 Maths Notes for Quick Revision. Here we have given NCERT Class 7 Maths Notes Chapter 3 Data Handling.

## CBSE Class 7 Maths Notes Chapter 3 Data Handling

Data Handling Class 7 Notes
Collection and Organisation of data in a particular manner makes it easier for us to understand and interpret data.

Before collecting data, we need to know what we would use it for.
Examples

• Performance of your class in Mathematics.
• Performance of India in football or in cricket.
• Female literacy rate in a given area, or
• The number of children below the age of five in the families around you.

Average is a number that represents or shows the central tendency of a group of observations of data.

The arithmetic mean (AM) or simply mean is defined as follows:
$$Arithmeticmean=\frac { Sum\quad of\quad all\quad observations }{ Number\quad of\quad observations }$$

Mean always lies between the greatest and smallest observation of the data.

Range is the difference between the highest and the lowest observation of the data. i.e. Range = Highest observation – Lowest observation

Mode of a set of observation is the observation that occurs, the most often e.g. 2 is the mode of a set of numbers 1, 1, 2, 4, 3, 2, 1, 2, 2, 4.

Median refers to the value which lies in the middle of the data with half of the observations above it and the other half below it.
e.g. 24, 36,46,17,18, 25, 35 is given data.
Firstly, data is to arranged in ascending order i.e. 17,18, 24,25, 35,36, 46.
Since the median is the middle observation, therefore 25 is the median.

If the data has an odd number of items, then the median is the middle number.

If the data has an even number of items, then the median is mean of two middle numbers.

A bar graph is a representation of numbers using bars of uniform widths.

Mode of the data is the longest bar if the bar represents frequency.

Double bar graphs help to compare two collections of data at a glance.

The situation that may or may not happen, have a chance of happening.
$$Probabilityofanevent=\frac { Number\quad of\quad favourable\quad outcomes }{ Total\quad number\quad of\quad outcomes\quad in\quad the\quad experiment }$$

Probability of an event which has no chance of happening is ‘0’.

Probability of an event which is bound to happen is 1.

Data Handling Class 7 Notes Pdf
Collecting Data

A given collection of data may not give us a piece of the specific information related to that data. Before collecting data, we need to know what we would use it for.

Organisation of Data
After the collection of data, we have to record and organize it.
Many kinds of data we come across are put in tabular form. Our school rolls, progress report, index in the notebooks, temperature record and many others are all in tabular form. Similarly, census record, a record of the values of shares, the record of DA, the record of HRA, are all in tabular form.
When we put data in a proper table, it becomes more meaningful. We can then interpret the data and take some inferences from them.

Class 7 Data Handling Notes
Representative Values

In our day-to-day life, we come across many statements that involve the term ‘average’. Average is a number indicating the representative of the central value of a group of observations or data. This representative value or central value is known as measure of central tendency.
Different forms of data need different forms of representative or central value to describe it.

Notes On Data Handling Class 7
Arithmetic Mean

The most common representative value is the arithmetic mean or the mean.
Rule: To find the mean, we find the sum of all the observations and divide this by the number of observations.
Result:
(i) The mean of several observations is the value which is equally shared out among all the observations.
(ii) The mean lies in between the greatest and the smallest observation.

Data Handling Notes For Class 7
Range

Range = Highest observation – Lowest observation

Mode
The mode of a set of observations is the observation that occurs most often.

Mode of Large Data
Putting the same observations together and counting is not easy if the number of observations is large. In such cases, we tabulate the data. Tabulation can begin by putting tally marks and finding the frequency.

Class 7 Maths Chapter 3 Notes Pdf
More than one Mode

A set of numbers can have more than one mode.
For example: For numbers 2, 2, 2,3, 3, 4, 5, 5, 5, 6,6, 8 ; 2 and 5 both occur highest (three) times.
Therefore, they both are the modes of the data.

Median
Median is the middle most observation of the data arranged in ascending or descending order.

Class 7 Maths Data Handling Notes
Use of Bar Graphs with a Different Purpose

By looking at the bar graph, we can make deductions about the data.
For example, we can say that the mode is longest bar if the bar represents the frequency.

Choosing a Scale
We should choose a proper scale so that all the data may be represented on the available graph paper.

Class 7 Maths Chapter 3 Notes
Drawing a double bar graph

These are used when we have to make comparisons between two collections of data at a glance.

Chance
Chance predicts simply a possibility.

7th Standard Data Handling Notes
What is Probability?

Probability is the measure of the chance of a particular event. It is measured as
$$\frac { no.\quad of\quad favourable\quad outcomes }{ no.\quad of\quad all\quad possible\quad outcomes }$$
Note: Two outcomes are said to be equally likely if we cannot expect one in preference to the other.

We hope the given CBSE Class 7 Maths Notes Chapter 3 Data Handling Pdf free download will help you. If you have any query regarding NCERT Class 7 Maths Notes Chapter 3 Data Handling, drop a comment below and we will get back to you at the earliest.

## Playing with Numbers Class 8 Notes Maths Chapter 16

CBSE Class 8 Maths Notes Chapter 16 Playing with Numbers Pdf free download is part of Class 8 Maths Notes for Quick Revision. Here we have given NCERT Class 8 Maths Notes Chapter 16 Playing with Numbers.

## CBSE Class 8 Maths Notes Chapter 16 Playing with Numbers

Any two digit number can be written as ab, where a and b are its tens and one’s digit respectively.

A 2-digit number is of the form 10a + b, where a is any whole number from 1 to 9 and b is any whole number from 0 to 9.

A 3-digit number is of the form 100a + 10b + c, where a is any whole number from 1 to 9, b is any whole number from 0 to 9 and c is any whole number from 0 to 9.

Playing With Numbers Class 8 Notes
Test of Divisibility:

• A number is divisible by 2 only when it’s unit digit is even.
• A number is divisible by 3 only when the sum of its digits is divisible by 3.
• A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
• A number is divisible by 5 only when it’s unit digit is 0 or 5.
• A number is divisible by 6 if it is divisible by both 2 and 3.
• A number is divisible by 8 if it is divisible by both 2 and 4.
• A number is divisible by 9 only when the sum of its digits is divisible by 9.
• A number is divisible by 10 if it’s unit digit is zero.

A number is even or odd according to it’s one’s digit.

Numbers in General Form
The general form of numbers helps us in solving puzzles or number games. A two digit number ab can be written in general form as ab = 10a + b.

Playing With Numbers Class 8 Notes Pdf
Games With Numbers

• Reversing the digits-two digit number
• Reversing the digits-three digit number
• Forming three-digit numbers with given three-digits

Letters for Digits
Here, we have puzzles in which letters are used in place of digits in an arithmetic ‘sum’, and the problem is to find out the digit represented by the letter used. We shall confine here to the problems of addition and multiplication.
The following rules are followed while solving such puzzles.
Rules

• Each letter must stand for just one digit. Each digit must be represented by just one letter.
• The first digit of a number cannot be zero.

Class 8 Maths Chapter 16 Notes
Tests of Divisibility

Here, we shall go into the ‘why’ aspect of the various tests of divisibility. We shall find that the reasons for the divisibility of the numbers by 10, 5, 2, 9 or 3 can be given by writing the numbers in their general form.

Divisibility By 10
A number is divisible by 10 when it’s ones digit is 0.

Playing With Numbers Notes Class 8
Divisibility By 5

A number is divisible by 5 when it’s one’s digit is either 0 or 5.

We hope the given CBSE Class 8 Maths Notes Chapter 16 Playing with Numbers Pdf free download will help you. If you have any query regarding NCERT Class 8 Maths Notes Chapter 16 Playing with Numbers, drop a comment below and we will get back to you at the earliest.

## Introduction to Graphs Class 8 Notes Maths Chapter 15

CBSE Class 8 Maths Notes Chapter 15 Introduction to Graphs Pdf free download is part of Class 8 Maths Notes for Quick Revision. Here we have given NCERT Class 8 Maths Notes Chapter 15 Introduction to Graphs.

## CBSE Class 8 Maths Notes Chapter 15 Introduction to Graphs

The x-coordinate of a point is its distance from y-axis.

The y-coordinate of a point is its distance from x-axis.

The coordinates of the origin are (0, 0).

The x-coordinate of every point on y-axis is zero.

The y-coordinate of every point on x-axis is zero.

A bar graph is used to show comparison among categories.

A pie graph is used to compare parts of a whole.

A histogram is a bar graph that shows data in intervals.

A line graph displays data that changes continuously over periods of time.

A line graph which is a whole unbroken line is called a linear graph.

Fixing a point on the graph sheet we need, x-coordinate and y-coordinate.

The relation between dependent variable and independent variable is shown through a graph.

The purpose of the graph is to show numerical facts in visual form for their better and quick understanding. It is specially very useful when there is a trend or comparison to be shown.

A Bar Graph
It consists of two or more parallel vertical (or horizontal) bars (rectangles).

A Pie Graph (or A Circle-Graph)
It is used to compare parts of a whole. The circle represents the whole.

A Histogram
It is a bar graph showing data in intervals. It has adjacent bars over the intervals.

Linear Graphs
Location of a Point
For locating a point on the graph sheet, we need its x-coordinate and y-coordinate.

Coordinates
x-coordinate of a point reveals how much we have to move from origin O to right or left along the x-axis ; whereas y-coordinate of a point reveals how much we have to move above or below O along the y-axis.

Some Applications
In our daily life, we observe two quantities that are interrelated i.e., the change in one quantity is accompanied by a change in the other quantity.

For example more the number of days a labourer works, more the wages he gets. More the sugar we purchase, more the amount we have to pay.

In the first case, the number of days is called the independent variable (or control variable) and the wages is called the dependent variable.

Similarly, in the second case, the amount of sugar is the independent variable whereas the money paid is the dependent variable.

The relation between the independent and dependent variables can be shown by a graph.

We hope the given CBSE Class 8 Maths Notes Chapter 15 Introduction to Graphs Pdf free download will help you. If you have any query regarding NCERT Class 8 Maths Notes Chapter 15 Introduction to Graphs, drop a comment below and we will get back to you at the earliest.

## Super Senses – CBSE Notes for Class 5 EVS

CBSE Notes Class 5 EVS chapter 1 revision becomes an easy task during the annual exam. Students who find it challenging to understand the basics of the chapter must practice all the essential questions to understand better. These crucial questions and answers on Super Senses simple and conceptual questions that are prepared by subject experts for the students to study well for the final exams. https://meritbatch.com/super-senses-cbse-notes-class-5-evs/

## Super Senses – CBSE Notes for Class 5 EVS

Super Senses Class 5 Notes
Summary:

• Animals have different senses.
• They can see, hear, taste, smell and feel.
• Some animals can see their prey from far away.
• Some animals can hear the faintest sound.
• Some animals can find their friends by their smell.
• Ears stood up: Became alert.
• Tsunami: A series of ocean waves produced by earthquakes or underwater landslide.

## Building With Bricks – CBSE Notes for Class 4 Maths

These are the Parts And Wholes Class 4 Notes Maths Chapter 1 prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days. Download CBSE Notes Class 4 Maths for chapter 1 in PDF format for free. https://meritbatch.com/building-with-bricks-cbse-notes-for-class-4-maths/

## Building With Bricks – CBSE Notes for Class 4 Maths

Summary:

• There are six faces in a brick.
• There are lakhs of brick kilns in India.
• Brick is made with soil dug from earth.

## How Big? How Heavy? – CBSE Notes for Class 5 Maths

These are the How Big? How Heavy? Class 5 Notes Maths Chapter 14 prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days. Download CBSE Notes Class 5 Maths for chapter 14 in PDF format for free. https://meritbatch.com/big-heavy-cbse-notes-class-5-maths/

## How Big? How Heavy? – CBSE Notes for Class 5 Maths

Summary:

• 1 kg = 1000 g
• A cube has equal length, width and height
• Volume of cuboid = (length x breadth x height) cubic unit
• Volume of cube = (Edge x Edge x Edge) cubic unit
• The faces of a cuboid are rectangular in shape.
• The faces of a cube are square in shape.

## Ways To Multiply And Divide – CBSE Notes for Class 5 Maths

These are the Ways To Multiply And Divide Class 5 Notes Maths Chapter 13 prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days. Download CBSE Notes Class 5 Maths for chapter 13 in PDF format for free. https://meritbatch.com/ways-to-multiply-and-divide-cbse-notes-class-5-maths/

## Ways To Multiply And Divide – CBSE Notes for Class 5 Maths

Summary:

• If you are given the cost of 1 article and asked to find the cost of more. You need to multiply them.
• If the cost of more articles together is given and you need to find the cost of 1 article or less, then you need to divide.
• Dividend = Quotient x Divisor + Remainder
• If remainder is zero then the divisor is the multiple of the dividend.

## Area and Its Boundary – CBSE Notes for Class 5 Maths

These are the Area and Its Boundary Class 5 Notes Maths Chapter 11 prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days. Download CBSE Notes Class 5 Maths for chapter 11 in PDF format for free. https://meritbatch.com/area-boundary-cbse-notes-class-5-maths/

## Area and Its Boundary – CBSE Notes for Class 5 Maths

Summary:

• Rectangle
Area of rectangle = Length x Breadth
Perimeter = 2 (length + breadth)
• Square
Area of square = Side x Side
Perimeter = 4 x Side
You can find the area of rectangle and square by splitting them into small boxes of 1 square cm.
Area of irregular shape can be obtained by counting the number of complete, half and more than half squares.

## Boxes And Sketches – CBSE Notes for Class 5 Maths

These are the Boxes And Sketches Class 5 Notes Maths Chapter 9 prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days. Download CBSE Notes Class 5 Maths for chapter 9 in PDF format for free. https://meritbatch.com/boxes-sketches-cbse-notes-class-5-maths/

## Boxes And Sketches – CBSE Notes for Class 5 Maths

Summary:

• 3-dimensional shapes: Shapes having length, breadth and height are called three dimensional shapes, e.g. cube, cuboid, boxes, etc.
• 2-dimensional shapes: Shapes having length and breadth only are called two dimensional shapes, e.g. square, rectangle, etc.
• We represent 3d shapes on the paper in 2D. The representation is done by nets.
• There are three different views of a drawing:
(a) From the top,
(b) from the front and
(c) from the side.

## Be My Multiple, I’ll Be Your Factor – CBSE Notes for Class 5 Maths

These are the Be My Multiple, I’ll Be Your Factor Class 5 Notes Maths Chapter 6 prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days. Download CBSE Notes Class 5 Maths for chapter 6 in PDF format for free. https://meritbatch.com/multiple-ill-factor-cbse-notes-class-5-maths/

## Be My Multiple, I’ll Be Your Factor – CBSE Notes for Class 5 Maths

Summary:

• Multiple: Multiple means to write the table of that number.
For example:
Multiples of 2: 2, 4, 6, 8, 10,12,
Multiples of 5: 5,10,15, 20, 25,
• Here, 10 is the lowest or smallest common multiple of 2 and 5.
• Factor: A number which can divide another number exactly is called the factor of the second number.
For example; the number 36 can be exactly divided by following numbers:
1, 2, 3, 4, 6, 9,12, 18 and 36
It means that these numbers are the factors of 36.

## Quadratic Equations Class 10 Notes Maths Chapter 4

CBSE Class 10 Maths Notes Chapter 4 Quadratic Equations Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 4 Quadratic Equations. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

## CBSE Class 10 Maths Notes Chapter 4 Quadratic Equations

A quadratic polynomial of the form ax² + bx + c, where a ≠ 0 and a, b, c are real numbers, is called a quadratic equation
when ax² + bx + c = 0.
Here a and b are the coefficients of x² and x respectively and ‘c’ is a constant term.

Any value is a solution of a quadratic equation if and only if it satisfies the quadratic equation.

The roots, i.e., α and β of a quadratic equation ax² + bx + c = 0 are given
by $$\frac { -b\pm \sqrt { D } }{ 2a }$$ or $$\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2a }$$ provided b² – 4ac ≥ 0.

Here, the value b² – 4ac is known as the discriminant and is generally denoted by D. ‘D’ helps us to determine the nature of roots for a given quadratic equation. Thus D = b² – 4ac.

The rules are:

1. If D = 0 ⇒ The roots are Real and Equal.
2. If D > 0 ⇒ The two roots are Real and Unequal.
3. If D < 0 ⇒ No Real roots exist.

If α and β are the roots of the quadratic equation, then Quadratic equation is x² – (α + β) x + αβ = 0 Or x² – (sum of roots) x + product of roots = 0

where, Sum of roots (α + β) = $$\frac { -coefficient\quad of\quad x }{ coefficient\quad of\quad { x }^{ 2 } } =\frac { -b }{ a }$$

Product of roots (α x β) = $$\frac { coefficient\quad term }{ coefficient\quad of\quad { x }^{ 2 } } =\frac { c }{ a }$$