Statistics – Measures of dispersion: Variance Variance(σ2 ) is a measure of how data points differ from the mean. It is defined as the average of the squared deviations for data set values: First, the formula says to subtract the mean from each of the scores. The difference of these quantities is called a deviate … Read more
Statistics – Measures of dispersion: Mean deviation A mean value is defined as the arithmetic average with which you are the most familiar.Another way to describe the variability of a set of data is to use its mean absolute deviation. The mean absolute deviation of a data set is the average variation between each data … Read more
Unit VI: Statistics and Probability Chapter 1: Statistics – Measures of dispersion: Range In statistics, there are 4 values considered to measure the central tendency and dispersion. The measure of location or central tendency is a mid-value that the data set is grouped around. It gives an average value. Central tendency Definition Mid-range Mean … Read more
Validating the statements involving the connecting words difference between contradiction, converse and contrapositive Rule 1: If p and q are mathematical statements, then to show that ‘p and q’ are true, follow the steps below: Show that p is a true statement Show that q is a true statement For statements with ‘or’ Rule 2: … Read more
Mathematical reasoning is required to determine if a mathematical argument is correct or incorrect in order to construct mathematical arguments. There are two types of reasoning identified in mathematics: deductive and inductive. Inductive reasoning requires processing from a series of specific cases to a general statement. The conclusion in an inductive argument is not guaranteed … Read more
A polynomial of degree n has at most n roots such that the cubics have at most 3 roots; quadratics (degree 2) have at most 2 roots and so on. Linear equations area slight exception in that they always have one root. Constant equations have constant integers. The first derivative of a polynomial function of … Read more
Definition of derivative, relate it to the slope of the tangent of a curve, derivative of the sum, difference, product and quotient of functions Differentiation relates to the measurement of change. For a linear function such as y = mx + b where b is the y-intercept and m is the constant slope. Here m … Read more
Trigonometric functions are continuous at all points Tangent and secant are flowing regularly everywhere in their domain, which is the combination of all exact numbers. Let a be a real number in the domain of a given trigonometric function, then $\lim _{x\to a}\sin x=\sin a$ $\lim _{x\to a}\cos x=\cos a$ $\lim _{x\to a}\tan x=\tan a$ … Read more
Let p be a polynomial function of x and c be a real number,the limit of p (x) as x approaches c does not depend on the value of f at x = c. It may happen, however, that the limit is precisely p (c).In such cases, the limit can be evaluated by direct substitution … Read more
You have already known that there is a very little difference between exponential and logarithmic functions. It is however important to recognize the most suitable ways to deal with these. Now, you may already know that the domain of a function is the set of probable inputs and also known as the x values. Also, … Read more