Frequency Tables
The frequency of a particular data value is the number of times the data value occurs.
For example, if four students have a score of 80 in mathematics, and then the score of 80 is
said to have a frequency of 4.
The frequency of a data value is often represented by f.
A frequency table is constructed by arranging...
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Frequency Tables The frequency of a particular data value is the number of times the data value occurs. For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f. A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies. Example 5 The marks awarded for an assignment set for a Year 8 class of 20 students were as follows: 6 7 5 7 7 8 7 6 9 7 4 10 6 8 8 9 5 6 4 8 Present this information in a frequency table. Solution : To construct a frequency table, we proceed as follows: Frequency Tables Know More About Define Regression. Math. Tutorvista. com Page No. :- 1/5
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Graphing a Circle
Definition of Circle Graph
A Circle Graph is a graph in the form of a circle that is divided into sectors, with each sector
representing a part of a set of data.
Example of Circle Graph
In the example shown below, the circle graph shows the percentages of people who like
different fruits.
Each sector in the circle...
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Graphing a Circle Definition of Circle Graph A Circle Graph is a graph in the form of a circle that is divided into sectors, with each sector representing a part of a set of data. Example of Circle Graph In the example shown below, the circle graph shows the percentages of people who like different fruits. Each sector in the circle graph represents a separate percentage of people that like the respective fruit. A circle graph is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length"> arc length of each sector and consequently its central angle and area, is proportional to the quantity it represents. When angles are measured with 1 turn as unit then a number of percent is identified with the same number of cent turns. Graphing a Circle Know More A0bout Combination and Permutation Math. Tutorvista. com Page No. :- 1/5
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Graphing Lines
Graphing linear equations is pretty simple, but only if you work neatly.
If you re messy, you ll
often make extra work for yourself, and you ll frequently get the wrong answer.
I ll walk you
through a few examples.
Follow my pattern, and you should do fine.
Graph y = 2x + 3
First, you draw what is called a "T-chart":...
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Graphing Lines Graphing linear equations is pretty simple, but only if you work neatly. If you re messy, you ll often make extra work for yourself, and you ll frequently get the wrong answer. I ll walk you through a few examples. Follow my pattern, and you should do fine. Graph y = 2x + 3 First, you draw what is called a "T-chart": it s a chart that looks a bit like the letter "T": The left column will contain the x-values that you will pick, and the right column will contain the corresponding y-values that you will compute. Label the columns: The first column will be where you choose your input (x) values; the second column is where you find the resulting output (y) values. Together, these make a point, (x, y). Pick some values for x. It s best to pick at least three value, to verify (when you re graphing) that you re getting a straight line. ("Linear" equations, the ones with just an x and a y, with no squared variables or square-rooted variables or any other fancy stuff, al
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Lower Quartile
Definition of Quartiles
Quartiles are values that divide a set of data into four equal parts.
More about Quartiles
A data set has three quartiles: the lower quartile, the median of the data set, and the upper
quartile.
Median: The median divides a data set into two equal parts.
Lower quartile: Median of the lower half...
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Lower Quartile Definition of Quartiles Quartiles are values that divide a set of data into four equal parts. More about Quartiles A data set has three quartiles: the lower quartile, the median of the data set, and the upper quartile. Median: The median divides a data set into two equal parts. Lower quartile: Median of the lower half of the data. Upper quartile: Median of the upper half of the data. Examples of Quartiles The owner of a super market recorded the number of customers who came into his store each hour in a day. The results were 12, 8, 10, 7, 15, 3, 6, 7, 12, 8, and 9. The ascending order of the data is 3, 6, 7, 7, 8, 8, 9, 10, 12, 12, 15. Lower Quartile Know More A0bout How to Calculate the Standard Deviation Math. Tutorvista. com Page No. :- 1/5
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Omitted Variable Bias
In statistics, omitted-variable bias (OVB) occurs when a model is created which incorrectly
leaves out one or more important causal factors.
The bias is created when the model
compensates for the missing factor by over- or under-estimating one of the other factors.
More specifically, OVB is the bias that...
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Omitted Variable Bias In statistics, omitted-variable bias (OVB) occurs when a model is created which incorrectly leaves out one or more important causal factors. The bias is created when the model compensates for the missing factor by over- or under-estimating one of the other factors. More specifically, OVB is the bias that appears in the estimates of parameters in a regression analysis, when the assumed specification is incorrect, in that it omits an independent variable (possibly non-delineated) that should be in the model. Effects on Ordinary Least Square Gauss–Markov theorem states that regression models which fulfill the classical linear regression model assumptions provide the best, linear and unbiased estimators. With respect to ordinary least squares, the relevant assumption of the classical linear regression model is that the error term is uncorrelated with the regressors. The presence of omitted variable bias violates this particular assumption. The violation causes
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How to do Integrals
Integration is an important part of calculus.
Integrals include single integral, double integral,
and multiple integrals.
Various types of integral are used to find surface area and the volume of geometric solids.
The double integral, triple integral
mostly used Gauss divergence theorem, Stokes theorem in vector...
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How to do Integrals Integration is an important part of calculus. Integrals include single integral, double integral, and multiple integrals. Various types of integral are used to find surface area and the volume of geometric solids. The double integral, triple integral mostly used Gauss divergence theorem, Stokes theorem in vector calculus. The Gauss divergence theorem produces results which relates the flow of the vector field vector field through a surface to the behavior of the vector field within the surface. Integration Definition Integration is a process of the summation of a product. In fact, the integration symbol ∫ is actually an elongated S, the S meaning a summation. Consider a function f(x) when it undergoes an infinitesimal change of dx. The product of the function and the infinitesimal change at any point is f(x)dx. In other words, it is the area of an infinitely small rectangle of the height f(x) and width dx. How to do Integrals Know More About Define Correla
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Derivative of a Function
The derivative of a function at a chosen input value describes the best linear approximation of
the function near that input value.
For a real-valued function of a single real variable, the
derivative at a point equals the slope of the tangent line to the graph of the function at that
point.
In higher...
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Derivative of a Function The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus. Differentiation is a method to compute the rate at which a dependent output y changes with respect to the change in the independent input x. This rate of change is called the derivative
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Difference Quotient Examples
The difference quotient is used in the derivative.
Dividing function difference from the
difference of point is called as the difference quotient it is otherwise known as Newton s
quotient.
X and Y are the two distinct points on the graph of function f.
A line passing through the 2
points X (x, f(x)) and...
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Difference Quotient Examples The difference quotient is used in the derivative. Dividing function difference from the difference of point is called as the difference quotient it is otherwise known as Newton s quotient. X and Y are the two distinct points on the graph of function f. A line passing through the 2 points X (x, f(x)) and Y ((x + h), f(x + h)), the formula to find difference quotient is [f(x+h)−f(x)]h The skill to set up and simplify difference quotients is a necessary help for calculus students. This is from the difference quotient that the basic formulas for derivatives are developed. X and Y are points on the graph of f. A line passing all the way through the 2 points X (x, f(x)) and Y(x+h, f(x+h)) is called a secant line. The derivative of (4x - 2)/(x^2 + 1) is: Difference Quotient Examples Know More About Partial Differential Equation Math. Tutorvista. com Page No. :- 1/5
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Instantaneous Rate of Change Formula
At the particular point, the rate of change is called as instantaneous rate of change ,which is
same as the derivative values at the same point.
If we consider a function, this rate of change
at a particular point is same as slope of the tangent line at the same point which is the slope of
the...
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Instantaneous Rate of Change Formula At the particular point, the rate of change is called as instantaneous rate of change ,which is same as the derivative values at the same point. If we consider a function, this rate of change at a particular point is same as slope of the tangent line at the same point which is the slope of the curve. When the object is travelling along a straight line, Average velocity is the average rate of change of place with respect to time. This method is known as differentiation with the fundamental theorem of calculus: lim as h->0 of f(x + h) = ( f(x + h) - f(x) ) / h There have been rules that have been formed by this formula, depending on the type of function given. Note: shows it is the rate of change function: Some basic rules: y = ax^n (where a is just a constant) y = n ax^(n - 1) where n 0 Product rule: y = f(x)g(x) y = f (g)g(x) + f(x)g (x) Quotient rule: y = f(x)/g(x) y = [f (g)g(x) - f(x)g (x)] / [g(x)]^2 Chain rule: y = f(g(x)) y = f (g(x)
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Linear Approximation Examples
Introduction
By now we have seen many examples in which we determined the tangent line to the graph of
a
function f(x) at a point x = a.
A linear approximation (or tangent line approximation) is
the simple idea of using the equation of the tangent line to approximate values of f(x) for x
near
x = a.
A...
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Linear Approximation Examples Introduction By now we have seen many examples in which we determined the tangent line to the graph of a function f(x) at a point x = a. A linear approximation (or tangent line approximation) is the simple idea of using the equation of the tangent line to approximate values of f(x) for x near x = a. A picture really tells the whole story here. Take a look at the gure below in which the graph of a function f(x) is plotted along with its tangent line at x = a. Notice how, near the point of contact (a; f(a)), the tangent line nearly coincides with the graph of f(x), while the distance between the tangent line and graph grows as x moves away from a. Linear approximation is a part of calculus, which comes under mathematics. Here, we do the approximation of normal function with the help of Linear Function. It is mainly used in finite differences to solve the first order method to simplify the problem or approximate the result of the equation. The process
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The Fundamental Theorem of Calculus
Through the examples we looked at for the area under graphs of functions, we were led to an
interesting observation: there seems to be a relationship between the process of integration,
which is just a fancy way of performing sums, and the process of differentiation.
In fact, this
observation is the...
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The Fundamental Theorem of Calculus Through the examples we looked at for the area under graphs of functions, we were led to an interesting observation: there seems to be a relationship between the process of integration, which is just a fancy way of performing sums, and the process of differentiation. In fact, this observation is the one basic fact which underlies almost all of our work in this course. Consequently, we will give it a name which indicates its importance: The Fundamental Theorem of Calculus. What does the Fundamental Theorem mean? Before we jump in and tell you about the theorem, we will try and give you an intuitive feel for it through a demonstration. We have seen already that the definite integral of a positive function can be interpreted as the area under the graph of the function. But what about functions which are negative? There s a pretty simple explanation in that case as well. Remember that the definite integral is given by a sum where the points are for
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Algebraic Equation Solver
Algebra equations are the equations of the form algebraic variables with some numerical coefficient.
Algebra equation contains the terms like numbers, integers, fractions, roots,
exponents, ratios, graphing etc.
Pre algebra equation is the simple equation which can be solved easily without any complex...
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Algebraic Equation Solver Algebra equations are the equations of the form algebraic variables with some numerical coefficient. Algebra equation contains the terms like numbers, integers, fractions, roots, exponents, ratios, graphing etc. Pre algebra equation is the simple equation which can be solved easily without any complex calculations. Linear equation is an algebraic equation in which each term is either a constant or the product of a constant and with a single variable. It contains one or more variables. It occurs with great regularity in applied mathematics. Algebra Equation Solver Algebra equation solver is to solve the equation and to get the value of variables. The following are the important things that need to be noted down in algebra equations Variables : The variable is the important thing that needs to be considered in equations. Operations : Operations such as (+, -, x, /) are the operations that plays an important role solving equations. Algebraic Equation Sol
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Degree of a Polynomial
The degree of polynomial is the greatest exponent of a term.
The greatest exponent should
have a non-zero coefficient in a polynomial expressed as a sum or difference of terms which
is commonly known as Canonical form.
The sum of the powers of all variables in the term is the degree of the polynomial.
The...
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Degree of a Polynomial The degree of polynomial is the greatest exponent of a term. The greatest exponent should have a non-zero coefficient in a polynomial expressed as a sum or difference of terms which is commonly known as Canonical form. The sum of the powers of all variables in the term is the degree of the polynomial. The degree can also be specified as order. The degree of polynomial is for the single variable or the combination of two or more variables with the powers. Properties of Degree of Polynomial According to the degree of polynomials the names are assigned. Below listed are the degree of polynomials: --- The name of the zero degree polynomial is constant. --- The name of the 1 degree polynomial is linear. --- The name of the 2 degree polynomial is quadratic. --- The name of the 3 degree polynomial is cubic. --- The name of the 4 degree polynomial is quartic Degree of a Polynomial Know More About What is the Dependent Variable Math. Tutorvista. com Page No. :-
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Standard Form Math
Standard form is generally a syntax kind for expressing mathematical operations.
Learn about
the concept here or you can also connect to an online tutor anytime and thus gain your
answers to math problems regarding standard form.
Get your help now.
Below is explained
about standard form in math, algebra and...
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Standard Form Math Standard form is generally a syntax kind for expressing mathematical operations. Learn about the concept here or you can also connect to an online tutor anytime and thus gain your answers to math problems regarding standard form. Get your help now. Below is explained about standard form in math, algebra and equations. What is Standard Form? The definition of Standard form is that it is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 x 103 = 4000. So 4000 can be written as 4 × 103. Standard form is also used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form. Example: Write 50 400 000 000 000 in standard form: 50 400 000 000 000 = 5. 04 × 1013 It’s 1013 because the decimal point has been moved 13 places to the left to get the number to be 5. 04 Standard Form in Algebra Standard form algebra is used to write down the complex equations in a simple form i. e. to write a l
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What is Independent Variable
In this page we are going to discuss about independent variable.
Below you can see how we
define independent variable.
Independent variable definition :- In an algebraic equation, independent variable means a
variable whose values are Independent of changes.
In the values of other variables.
If y is...
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What is Independent Variable In this page we are going to discuss about independent variable. Below you can see how we define independent variable. Independent variable definition :- In an algebraic equation, independent variable means a variable whose values are Independent of changes. In the values of other variables. If y is dependent variable then x is said to be independent variables. For example, take x and y are two variable in the given algebraic equation. Here every value of x is definitely connected with any other value of y, then y value is said to be function of x value is called as an independent variable and y value is called as a “dependent” variable. y values are depending upon the values of x values. Therefore, y = x2 It means y is a dependent variable, Is the square of x value is independent variable. What is an Independent variable ? What is Independent Variable Know More About What is Standard Form Math. Tutorvista. com Page No. :- 1/5
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Writing Algebraic Expressions
Writing Algebraic expression for a word phrase for an expression.
When solving real world
problems will need to translate words into algebraic expressions.
Write an algebraic
expression is not a sentence.
Writing algebraic expressions are made up of symbols.
The
expressions represent one or more...
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Writing Algebraic Expressions Writing Algebraic expression for a word phrase for an expression. When solving real world problems will need to translate words into algebraic expressions. Write an algebraic expression is not a sentence. Writing algebraic expressions are made up of symbols. The expressions represent one or more quantity. Order of operations Order of operations with exponents Order of operations. Addition (a+b) Subtraction (a-b) Multiplication (ab) Division (a/b) Rules : Perform first calculations inside parentheses. All multiplications and divisions are working from left to right. Finally additions and subtractions are working from left to right. Writing Algebraic Expressions Know More About Definite Integral Math. Tutorvista. com Page No. :- 1/5
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How To Solve Absolute Value Equations
Learn absolute value equations concept.
The equation |x| = 4.
This means that x could be 4 or
x could be -4.
When you take the absolute value of 4, the solution is 4 and when you take the
absolute value of -4, the solution is also 4.
An absolute value problem, you have to get into
account that...
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How To Solve Absolute Value Equations Learn absolute value equations concept. The equation |x| = 4. This means that x could be 4 or x could be -4. When you take the absolute value of 4, the solution is 4 and when you take the absolute value of -4, the solution is also 4. An absolute value problem, you have to get into account that there can be two solutions that will make the equation true. Learning absolute value equation, you set the quantity inside the absolute value symbol equal to the positive and negative value on the other side of the equal symbol. Solve Absolute Value Equations Below are the examples on how to solve absolute value equations Example 1 : -|x + 1| = 4 Solution : The quantity inside the absolute value symbol can be equal to 4 or -4 x + 1 = 4 or x + 1 = - 4 Subtract 1 on both side of the given equation x + 1 - 1 = 4 - 1 or x + 1 - 1 = -4 - 1 x = 3 or x = -5 How To Solve Absolute Value Equations Know More About Polynomial Factoring Math. Tutorvista. com Page No
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Solve Algebra Equations
Algebra equations are the equations of the form algebraic variables with some numerical coefficient.
Algebra equation contains the terms like numbers, integers, fractions, roots,
exponents, ratios, graphing etc.
Pre algebra equation is the simple equation which can be
solved easily without any complex...
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Solve Algebra Equations Algebra equations are the equations of the form algebraic variables with some numerical coefficient. Algebra equation contains the terms like numbers, integers, fractions, roots, exponents, ratios, graphing etc. Pre algebra equation is the simple equation which can be solved easily without any complex calculations. Linear equation is an algebraic equation in which each term is either a constant or the product of a constant and with a single variable. It contains one or more variables. It occurs with great regularity in applied mathematics. Example on how to solve algebra equations: Solve Algebra equation 2x + 4 = 0 2x + 4 = 0 2x = - 4 x = −42 x = -2 Algebra Equation Solver Solve Algebra Equations Know More About Trinomial Factoring Math. Tutorvista. com Page No. :- 1/5
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