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Here we will learn how to solve different types of problems on plotting points in the xy 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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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 yintercept is c. By knowing the slope and yintercept for a line graph, the graph can be easily drawn
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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 yaxis because
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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 rightangled ∆MON, tan θ =
Continue reading "Slope of the Graph of y = mx + c  What is the Graph of y=mxc?"
If the graph of y = mx + c cuts the yaxis at P then OP is the yintercept of the graph, where O is the origin. If OP is in the positive direction of the yaxis, the intercept is positive. But if OP is in the negative direction of the yaxis, the intercept is negative.
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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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If the coordinates (x, y) of a point are given, one can plot in the Cartesian xy 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
Continue reading "Plotting a Point in Cartesian Plane  Determine the Quadrant "
The xaxis (XOX’) and yaxis (YOY’) divided the xy 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
Continue reading "Quadrants and Convention for Signs of Coordinates  Four Quadrants"
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.
Continue reading "Rectangular Cartesian Coordinates of a Point  Signs of Coordinates"
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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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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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 oneday 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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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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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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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.
Continue reading "Class Boundaries How to Find Class Boundaries? Statistics Dictionary"
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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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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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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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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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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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
Continue reading "Class Limits What is the Class Limit in Statistics?Find Class Limits"
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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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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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
Continue reading "Worksheet on Mean of Ungrouped Data  Find the Mean Weight/Expenditure"
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 =
Continue reading "Problems on Median of Ungrouped DataUngrouped Data to Find the Median"
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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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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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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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
Continue reading "Frequency of the Statistical DataFrequency of 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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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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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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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
Continue reading "Statistics and Statistical Data  Sample or Representative Data"
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
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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?
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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
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Gropu data are also represented by a curve called ogive or cumulativefrequency 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 frequencydistribution
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We will discuss about the method of constructing a frequency polygon with the help of a class marks. Step I: Prepare a frequencydistribution table overlapping intervals. Step II: Find the class marks of the class intervals and locate them on the horizontal axis
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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
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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
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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.
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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
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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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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`
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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 preprimary section, 1,200 children in th
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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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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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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.
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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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