Math Blog

Problems on Plotting Points in the x-y Plane | Plot the Points

Here we will learn how to solve different types of problems on plotting points in the x-y plane. 1. Plot the points in the same figure. (i) (3, -1), (ii) (-5, 0), (iii) (3, 4.5), (iv) (-1, 6), (v) (-2.5, -1.5) Solution: Draw two mutually perpendicular lines X’OX and Y’OY

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Drawing Graph of y = mx + c Using Slope and y-intercept | Examples

Here we will learn how to draw the graph of a linear relation between x and y is a straight line. So, the graph of y = mx + c is a straight line. We know its slope is m and y-intercept is c. By knowing the slope and y-intercept for a line graph, the graph can be easily drawn

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Graph of Standard Linear Relations Between x, y | Graph of y = x

Here we will learn how to draw the graph of standard linear relations between x, y. Graph of x = 0 Some of the orders pairs of values of (x, y) satisfying x = 0 are (0, 1), (0, 2), (0, -1), etc. All the points corresponding to these ordered pairs are on the y-axis because

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Slope of the Graph of y = mx + c | What is the Graph of y=mx-c?

The graph of y = mx + c is a straight line joining the points (0, c) and -c/m Let M = (-c/m, 0) and N = (0, c) and ∠NMX = θ. Then, tan θ is called the slope of the line which is the graph of y = mx + c. Now, ON = c and OM = c/m. Therefore, in the right-angled ∆MON, tan θ =

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y-intercept of the Graph of y = mx + c | How to Find y-intercept?

If the graph of y = mx + c cuts the y-axis at P then OP is the y-intercept of the graph, where O is the origin. If OP is in the positive direction of the y-axis, the intercept is positive. But if OP is in the negative direction of the y-axis, the intercept is negative.

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Coordinate Geometry Graph | Graph of Linear Relations Between x, y

Here we will learn how to draw Coordinate geometry Graph. When two variables x, y are related, the value(s) of one variable depends on the value(s) of the other variable. Let x, y be two variables related by 9x - 3y + 4 = 0. Then, y = 3x + $$\frac{4}{3}$$.

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Plotting a Point in Cartesian Plane | Determine the Quadrant

If the coordinates (x, y) of a point are given, one can plot in the Cartesian x-y plane by taking the following steps. Step I: Observe the signs of the coordinates and determine the quadrant in which the point should be plotted. Step II: Take a rectangular Cartesian frame of

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Nov 25, 2018

The x-axis (XOX’) and y-axis (YOY’) divided the x-y plane in four regions called quadrants. The region of the plane falling in the angle XOY is called the first quadrant. The region of the plane falling in the angle X’OY is called the second quadrant. The region of the plane

Rectangular Cartesian Coordinates of a Point | Signs of Coordinates

Take two intersecting lines XOX’ and YOY” in a plane which cut at O and are perpendicular to each other. Let P be a point in the plane. Draw perpendiculars from P to the line XoX’ and YoY’. Let them be PL and PM. Measure PL and PM in the same scale in mm, cm or m, etc.

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Coordinates of a Point | Cartesian Coordinate System | Ordered Pair

In elementary plane geometry a point is described by given it a name, such as P, Q or R. But in coordinate geometry, a point is described by its position in the plane. The position of a point is given by an ordered pair (a, b) of real numbers.

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Ordered Pair | First Coordinate | Second Entry or Second Coordinate

Let a and b be two real numbers. (a, b) is called a pair of real numbers a, b. But (a, b) is called an order pair if (a, b) is different from (b, a). In the ordered pair (a, b), a is called the first entry or first coordinate and b is called the second entry or second

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Independent Variables and Dependent Variables | Variable | Formula

If x stands for any of the real numbers from the set R then x is a variable over R. For example, if x is the over number in an one-day international cricket match of 50 overs then x is a variable over the set {1, 2, 3, 4, ...., 48, 49, 50}. Suppose, x is the side of a square

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Class Interval | Overlapping and Nonoverlapping Class Intervals

In order to express raw data in the form of grouped data we use classes (or class intervals) for the values of the variables. Depending upon the method of grouping data, class intervals can be divided into two categories. (i) Overlapping Class Intervals: If the values of a

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Tally Marks | Tally Mark Represents Frequency | Use of Tally Marks

We will discuss here how to use Tally marks. To count the number of times a value of the variable appears in a collection of data, we use tally mark ( / ). Thus tally mark represents frequency. Observe the tally marks and the corresponding frequencies:

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Class Boundaries |How to Find Class Boundaries? |Statistics Dictionary

Here we will learn class boundaries or actual class limits For overlapping class intervals, the class limits are also called class boundaries or actual class limits. In the case of nonoverlapping class intervals, the class limits are different from class boundaries.

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Cumulative Frequency | Frequency Distribution | Class Interval

Here we will learn cumulative frequency. The cumulative frequency of a value of a variable is the number of values in the collection of data less than or equal to the value of the variable. For example: Let the raw data be 2, 10, 18, 25, 15, 16, 15, 3, 27, 17, 15, 16.

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Constructing Frequency Distribution Tables | Classified / Unclassified

Here we will learn how to construct frequency distribution tables. Following is a collection of raw data showing the ages (in years) of 30 students of class. 14, 15, 14, 16, 15, 13, 17, 16, 17, 16, 17, 12, 13, 12, 14, 15, 16, 15, 18, 12, 17, 17, 18, 13, 14, 13, 16, 15

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Nonoverlapping Class Intervals into Overlapping Class Intervals

We will learn here how to convert nonoverlapping class intervals into overlapping class intervals. Conversion of Nonoverlapping Class intervals into Overlapping Class intervals: If the nonoverlapping class intervals are a - b, c - d, e - f, etc., the gaps between the

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Class Mark | Class Mark Statistics | What is Class Mark?

Here we will learn class mark. The class mark of a class interval = (Actual lower limit + Actual upper limit)/2 = (Sum of Class Boundaries)/2. For Example: The class mark of the overlapping class interval 10 – 20 = (10 + 20)/2 = 15.

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Class Size Statistics | What is Class Size? | Statistical Data

Here we will learn class size. The class size of an overlapping or nonoverlapping class interval = actual upper limit – actual lower limit = difference of class boundaries. For example: The class size of the overlapping interval 10 - 20 = Actual upper limit – actual lower

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Class Limits |What is the Class Limit in Statistics?|Find Class Limits

We will discuss here about the class limits. Let the class intervals for some grouped data 5 – 15, 15 – 30, 30 – 45, 45 – 60, etc. Here, all the class intervals are overlapping and the distribution is continuous. 5 & 15 are called the class limits of the class interval

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Frequency Distribution | Unclassified Frequency Distribution

In the above Table 1 we have an example of unclassified frequency distribution. It shows the number of students obtaining certain marks. For example, the table shows 4 marks were attained by 3 students, 20 marks were obtained by 7 students, etc. So the frequency of 4 marks

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Worksheet on Median of Ungrouped Data | Find the Median of Collection

Practice the questions given in the worksheet on median of ungrouped data. 1. Find the median of the following. (i) The first seven even natural numbers (ii) 5, 0, 2, 4, 3 (iii) 25, 22, 28, 23, 21, 27, 25, 24, 20 2. Find the median of the following. The first six odd natural

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Worksheet on Mean of Ungrouped Data | Find the Mean Weight/Expenditure

Practice the questions given in the worksheet on mean of ungrouped data. 1. Find the mean of the following. (i) The first five positive integers. (ii) The first six even natural numbers. 2. Find the mean of the following data. (i) 7, 9, 3, 5, 8, 6 (ii) 4, 11, 0, 5, 10

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Problems on Median of Ungrouped Data|Ungrouped Data to Find the Median

Here we will learn how to solve the different types of problems on median of ungrouped data. 1. The heights (in cm) of 11 players of a team are as follows: 160, 158, 158, 159, 160, 160, 162, 165, 166, 167, 170. The number of variates = 11, which is odd. Therefore, median =

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Problems on Mean of Ungrouped Data | Ungrouped Data to Find the Mean

Here we will learn how to solve the different types of problems on mean of ungrouped data. 1. (i) Find the mean of 6, 10, 0, 7, 9. (ii) Find the mean of the first four odd natural numbers. Solution: (i) We know that the mean of five variates

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Median of Raw Data |The Median of a Set of Data|How to Calculate Mean?

The median of raw data is the number which divides the observations when arranged in an order (ascending or descending) in two equal parts. Method of finding median Take the following steps to find the median of raw data. Step I: Arrange the raw data in ascending

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Mean of Ungrouped Data | Mean Of Raw Data | Mean of Arrayed Data

The mean of data indicate how the data are distributed around the central part of the distribution. That is why the arithmetic numbers are also known as measures of central tendencies. Mean Of Raw Data: The mean (or arithmetic mean) of n observations (variates)

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Frequency of the Statistical Data|Frequency of Set of Statistical Data

The frequency of a value of a variable is the number of times it appears in a collection of data. Example: What is the frequency of 12 in the following data? Solution: 12 appears thrice in the collection. So, the frequency of 12 is 3. Solved Example: The weights (in kg) of

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Range of the Statistical Data | Range of a Set of Statistical Data

The difference between the greatest and the least values of a variable in a collection of data is called the range of the data. For Example: In collection A, the greatest value of marks obtained is 90 while the least value of the same is 4. So, the range of the data = 90 - 4

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Statistical Variable |Variables in Statistics|Variables and Statistics

The quantity whose different values during observation constitute the collection of data is called a statistical variable. In collection A, the marks obtained by the students is a variable. If we denote the marks obtained by x then x is a variable in the collection.

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Representation of Data | Raw Data | Arrayed Data | Grouped Data

Collection A (shown below) represents the marks obtained by 50 students in a test of 100 marks. In the collection above, 80, 70, etc., are called the terms of the collection. Depending on the form of expression, data may be raw (i.e., ungrouped) or arrayed. I. Raw Data:

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Statistics and Statistical Data | Sample or Representative Data

Statics is that branch of mathematic which deals with the collection, classification, representation, analysis and interpretation on numerical data. The study of statistics started nearly 2000 years ago. Today statistics holds an important place in the fields of economics

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Problems on Cumulative-Frequency Curve | Problems on Ogive Graph

We will discuss here some of the problems on frequency polygon. The monthly salaries of 55 workers of a factory are displayed in the following ogive. Answer the following. (i) How many workers have a monthly salary UNDER $4000? (ii) How many workers have a monthly salary Continue reading "Problems on Cumulative-Frequency Curve | Problems on Ogive Graph" Sep 13, 2018 Problems on Frequency Polygon | Frequency Polygon Examples We will discuss here some of the problems on frequency polygon. 1. The frequency polygon of a frequency distribution is shown below. Answer the following about the distribution from the histogram. (i) What is the frequency of the class interval whose class mark is 15? Continue reading "Problems on Frequency Polygon | Frequency Polygon Examples" Sep 11, 2018 Problems on Histogram | Reading Histograms | Histograms Examples We will discuss here some of the problems on histogram. The histogram for a frequency distribution is given below. (i) What is the frequency of the class interval 15 – 20? (ii) What is the class intervals having the greatest frequenciey? (iii) What is the cumulative Continue reading "Problems on Histogram | Reading Histograms | Histograms Examples" Sep 10, 2018 Cumulative-Frequency Curve | Ogive | Method of Constructing on Ogive Gropu data are also represented by a curve called ogive or cumulative-frequency curve. As the name suggests, in this representation cumulative frequencies of different class intervals play an important role. Method of Constructing on Ogive: Prepare a frequency-distribution Continue reading "Cumulative-Frequency Curve | Ogive | Method of Constructing on Ogive" Aug 28, 2018 Method of Constructing Frequency Polygon with the Help of Class Marks We will discuss about the method of constructing a frequency polygon with the help of a class marks. Step I: Prepare a frequency-distribution table overlapping intervals. Step II: Find the class marks of the class intervals and locate them on the horizontal axis Continue reading "Method of Constructing Frequency Polygon with the Help of Class Marks" Aug 25, 2018 Method of Constructing a Frequency Polygon with the Help of Histogram Step I: Draw the histogram for the frequency distribution as explained above. Step II: Locate the midpoint of the top horizontal side of each rectangle in the histogram. Step III: Locate the middle points on the horizontal axis of two imaginary intervals of common size, one Continue reading "Method of Constructing a Frequency Polygon with the Help of Histogram" Aug 24, 2018 Frequency Polygon | Methods of Constructing a Frequency Polygon Grouped data are also represented by frequency polygons. A frequency polygon is a polygon whose vertices are at the midpoint of the tops of rectangles forming the histogram of the frequency distribution. These middle points correspond to the class marks of the corresponding Continue reading "Frequency Polygon | Methods of Constructing a Frequency Polygon" Aug 22, 2018 Histogram | Method of Constructing a Histogram | Creating a Histogram Grouped data are often represented graphically by histograms. A histogram consists of rectangles, each of which has breadth equal or proportional to the size of the concerned call interval, and height equal or proportional to the corresponding frequency. Continue reading "Histogram | Method of Constructing a Histogram | Creating a Histogram" Aug 20, 2018 Word Problems on Addition and Subtraction | Mixed Add & Subtract Solved examples on Word problems on addition and subtraction . 1. In a school there are 2,392 boys and 2,184 girls. Find the total number of students in the school. Solution: Number of boys in the school = 2392 Number of girls in the school = + 2184 Total students in the Continue reading "Word Problems on Addition and Subtraction | Mixed Add & Subtract" Aug 06, 2018 Worksheet on Word problem on Multiplication | Multiplication Facts Practice the worksheet on word problem on multiplication. 1. One complete set of class IV costs$264. How much money did a class of 42 children pay to the bookshop owner, if all of them bought their books from him? 2. One pair of football shoes costs \$ 628. Find the cost of

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Word Problems on Multiplication |3rd Grade Math|Multiplication Problem

Solved examples on word problems on multiplication.For a school trip 6 buses were hired. Each bus carried 42 children. How many children went on the trip? Solution: 2. The product of two numbers is 96. If one number is 8, find the other. Multiplicand × Multiplier = Product

Jul 25, 2018

Practice the worksheet on word problem on addition and subtraction. 1. In a village, there are 4,318 men, 3,624 women and 5,176 children. What is the total population of the village? 2. In a school, there are 860 children in the pre-primary section, 1,200 children in th

Making the Numbers From Given Digits | Write Smallest/Greatest Number

We can make numbers from the given digits. Let us see the rules. Rule I. To get the smallest number, arrange the digits in ascending order from left to right. Rule II. To get the greatest number, arrange the digits in descending order from left to right. Example: Write the

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Worksheet on Facts about Division | Division with Small Numbers

Practice the worksheet on facts about division. We know, dividend is always equal to the product of the divisor and the quotient added to the remainder. This will help us to solve the given questions. 1. Fill in the blanks: (i) Division is __ subtraction.

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Jul 13, 2018

Practice the worksheet on facts about multiplication. We know in multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the multiplier. This will help us to solve the given questions.

Worksheet on Facts about Subtraction | Subtraction with Small Numbers

Practice the worksheet on facts about subtraction. Subtraction with small numbers can be worked out horizontally and subtraction with large numbers is worked out vertically. 1. Fill in the missing numbers. (i) Take away 14 from 80 is ______ (ii) 150 decreased by 80 is ____

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