# Math Blog

### 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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### 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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###### Jul 12, 2018

Practice the worksheet on facts about addition. Addition of small numbers can be done horizontally and large numbers are added in vertical columns. 1. Fill in the missing number/word. (i) 4315 + 101 = 101 + ______ = ______ (ii) 1795 + 241 = 241 + ______

### Facts about Multiplication | Multiplication Operation | Multiplicand

We have learnt multiplication of numbers with 2digit multiplier. Now, we will learn more. Let us know some facts about multiplication. 1. In multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the

### Facts about Subtraction | Subtraction of Small Numbers|Solved Examples

The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction with small numbers can be worked out horizontally. Example: 8 – 5 = 3 24 – 4 =

###### Jul 11, 2018

The operation to find the total of different values is called addition. Let us know some facts about addition which will help us to learn to add 4-digit and 5-digit numbers. 1. Addition of small numbers can be done horizontally. Example: 6 + 2 + 3 = 11

### Facts about Division | Basic Division Facts | Learn Long Division

We have already learned division by repeated subtraction, equal sharing/distribution and by short division method. Now, we will read some facts about division to learn long division. 1. If the dividend is ‘zero’ then any number as a divisor will give the quotient as ‘zero’.

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### Expanded Form and Short Form of a Number | Numbers in Expanded Form

When we write a number as a sum of place value of its digits, the number is said to be in expended form and when we write a number using digits, the number is said to be in short form. There are 3 ways to write the expanded form. There are 3 ways to write the expanded form

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### Long Division | Division by One-Digit Divisor and Two-Digit Divisors

As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend one at a time starting with the highest place.

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### Multiplication of Matrices | How to Multiply Matrices? |Rules|Examples

Two matrices A and B are said to be conformable for the product AB if the number of columns of A be equal to the number of rows of B. If A be an m × n matrix and B an n × p matrix then their product AB is defined to be the m × p matrix whose (ij)th element is obtained by

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### Worksheet on Addition of Matrices | Find the Sum of Two Matrices | Ans

Practice the problems given in the worksheet on addition of matrices. If M and N are the two matrices of the same order, then the matrices are said conformable for addition, and their sum is obtained by adding the corresponding elements of M and N. 1. Find the sum of A and B

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### Properties of Scalar Multiplication of a Matrix |Scalar Multiplication

We will discuss about the properties of scalar multiplication of a matrix. If X and Y are two m × n matrices (matrices of the same order) and k, c and 1 are the numbers (scalars). Then the following results are obvious. I. k(A + B) = kA + kB II. (k + c)A = kA + cA III. k(cA)

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### Scalar Multiplication of a Matrix | Examples on Scalar Multiplication

The operation of multiplying variables by a constant scalar factor may properly be called scalar multiplication and the rule of multiplication of matrix by a scalar is that the product of an m × n matrix A = [aij] by a scalar quantity c is the m × n matrix [bij] where bij

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### Subtraction of Matrices | Examples on Difference of Two Matrices

We proceed to develop the algebra of subtraction of matrices. Two matrices A and B are said to be conformable for subtraction if they have the same order (i.e. same number of rows and columns) and their difference A - B is defined to be the addition of A and (-B).

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### Properties of Addition of Matrices | Commutative Law | Associative Law

We will discuss about the properties of addition of matrices. 1. Commutative law of addition of matrix: Matrix multiplication is commutative. This says that, if A and B are matrices of the same order such that A + B is defined then A + B = B + A. Proof: Let A = [aij]m × n

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### Addition of Matrices | Example on Sum of Two Matrices

We proceed to develop the algebra of matrices. Two matrices A and B are said to be conformable for addition if they have the same order (same number of rows and columns). If A = (aij)m, n and B = (bij)m,n then their sum A + B is the matrix C = (cij)m,n where cij = aij + bij

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### Triangular Matrix | Upper Triangular Matrix | Lower Triangular Matrix

There are two types of triangular matrices. 1. Upper Triangular Matrix: A square matrix (aij) is said to be an upper triangular matrix if all the elements below the principal diagonal are zero (0). That is, [aij]m × n is an upper triangular matrix if (i) m = n and (ii) aij

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### Height and Distance with Two Angles of Elevation | Solved Problems

We will solve different types of problems on height and distance with two angles of elevation. Another type of case arises for two angles of elevations. In the given figure, let PQ be the height of pole of ‘y’ units. QR be the one of the distance between the foot of the pole

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### Angle of Elevation | How to Find out the Angle of Elevation

We have already learnt about trigonometry in previous units in detail. Trigonometry has its own applications in mathematics and in physics. One such application of trigonometry in mathematics is “height and distances”. To know about height and distances, we have to start

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### Identity Matrix | Unit Matrix |If [d] is a scalar matrix then [d] = dI

A scalar matrix whose diagonal elements are all equal to 1, the identity element of the ground field F, is said to be an identity (or unit) matrix. The identity matrix of order n is denoted by In. A scalar matrix is said to be a unit matrix, if diagonal elements are unity.

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### Definition of Equal Matrices | Examples of Equal Matrices

Equality of two matrix: Two matrices [aij] and [bij] are said to be equal when they have the same number of rows and columns and aij = bij for all admissible values of i and j. Definition of Equal Matrices: Two matrices A and B are said to be equal if A and B have the same

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### Null Matrix | Null or Zero Matrix|Zero Matrix|Problems on Null Matrix

If each element of an m × n matrix be 0, the null element of F, the matrix is said to be the null matrix or the zero matrix of order m × n and it is denoted by Om,n. It is also denoted by O, when no confusion regarding its order arises. Null or zero Matrix: Whether A is a

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