Percentiles and Frequency Distributions

The concept of the median of a one-sample (univariate) data set was introduced in Statistics Defined. Here we seek to provide a deeper understanding for this measure of data location by showing that the median is a special case of the percentiles of a distribution. How does all this relate to probability ? Our aim Read more about Percentiles and Frequency Distributions[…]

Histograms with Unequal Class Intervals

Recall that a histogram is a powerful method for visualizing a quantitative data set in terms of its frequency distribution. It is a specialized form of bar chart in which there are no gaps between the bars: the base of each bar represents a specific class interval of the data in question. Also, the bars are sometimes referred Read more about Histograms with Unequal Class Intervals[…]

Transformed Trigonometric Functions

Two or more trig. function transformations are dealt with using the general equations:   y2 = asin[b(x – c)] + d  ,   acos[b(x – c)] + d ;   atan[b(x – c)] + d   EXAMPLE 1:      ;   a = 2  &  d = 3,   so  M = ;                                                                                                  Also,  m =   .   EXAMPLE Read more about Transformed Trigonometric Functions[…]

Composition of Functions

Given two functions, f(x) and g(x), we can combine them by the operations of addition, subtraction, multiplication, or division: the result will usually be a new function, h(x). If f(x) and g(x) are polynomials, for instance, their product is another polynomial of higher degree. Again if f(x) and g(x) are polynomials, their quotient is a Read more about Composition of Functions[…]

Trigonometric Equations

A trigonometric equation is an equation involving one or more trigonometric functions. Therefore the solution to a trigonometric equation is one or more angles. Most trigonometric equations at the secondary level can be analyzed in terms of simpler components.  So we offer the following comments on the most basic form of trig. equation.             The simple (linear Read more about Trigonometric Equations[…]

Piecewise Defined Functions

  A function is piecewise-defined if its domain consists of a finite number of pieces (subintervals) each with its own, possibly unique defining equation. The simplest example of a piecewise-defined function is the absolute value function, depicted below.     This function is described by the equation:  y = |x| , where |x| is defined Read more about Piecewise Defined Functions[…]