Discrete Wavelet Transformations: An Elementary Approach with Applications

APPENDIX A

BASIC STATISTICS

The material in Chapter 9 makes use of several ideas from basic statistics. We also use some simple descriptive statistics in the edge detection application in Section 6.4. In this appendix we review some basic statistical concepts.

A.1   DESCRIPTIVE STATISTICS

In Chapter 6 we make use of some basic descriptive statistics. We utilize the mean absolute deviation in Chapter 9. We start first with the definition of the mean.

Definition A.1 (Mean). Let x = (x₁, x₂, … , x_n) be a list of numbers. Then the mean is defined as

A second statistic that is used to measure the center of the data is the median. The median is a number x_med such that the number of data below x_med is equal to the number of data above x_med.

Definition A.2 (Median). Let x = (x₁, x₂, … , x_n) be a list of numbers. The median x_med is constructed by first sorting the values x₁, x₂, … , x_n from smallest to largest. Call this new list y = (y₁, y₂, … , y_n). If n is odd, we set . If n is even, we take the median to be the average of the two middle components. That is, x_med = (y_n/2 + y_n/2+l).            ...