Probability is a number of ways a certain event can occur to the number of possible outcomes. An outcome is one possible result of a probability and the act that leads to a single outcome that cannot be predicted with certainty is called an experiment. For instance, today there is a 45 The random experiment … Read more

Statistics – Analysis of frequency distributions with equal means but different variances The coefficient of variation is a measure of the relative variability (or consistency) of two or more data sets. It is calculated by taking the ratio of the standard deviation divided by the mean. It may also be expressed as a percentage to … Read more

Statistics – Measures of dispersion: Standard deviation Standard deviation (SD) is a measure of how each value in a data set varies or deviates from the mean. The standard deviation is calculated by deducing the square root of the variance. It is denoted with the same units as the original data. Assuming that all values … Read more

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