Chapter 1 – Introduction to Statistics
1-1 Review and Preview
* Data – are collections of observations, such as measurements, genders, or survey responses. (A single data is a called a datum, a term that does nog see very much use.)
* Statistics – is the science of planning studies and experiments; obtaining data; and then organizing, summarizing, presenting, analyzing, and interpreting those data and then drawing conclusion based on them.
* Population – is the complete collection of all measurements or data that are being considered.
* Census – is the collection of data from every member of the population.
* Sample – is a sub-collection of members selected from a ...view middle of the document...
Later in this book, we will use inferential statistics to make inferences, or generalizations, about a population.
3-2 Measures of Center
* The focus of this section is the characteristics of center of a data set. In particular, we present measures of center, including mean and median, as tools for analyzing data.
Part 1: Basic Concepts of Measures of Center
* Measure of Center – is a value at the center or middle of a data set.
* There are several different ways to determine the center, so we have different definitions of measures of center, including mean, median, mode, and midrange. We begin with the mean.
* The mean (or arithmetic mean) is generally the most important of all numerical measurements used to describe data, and it what most people call an average.
* Arithmetic mean, or the mean, of a set of data is the measure of center found by adding the data values and dividing the total by the number of data values.
* Important Properties of the Mean
* Sample means drawn from the same population tend to vary less than other measures of center.
* The mean of a data set uses every data value.
* A disadvantage of the mean is that just one extreme value (outlier) can change the value of the mean substantially. (Since the mean cannot resist substantial changes caused by extreme values, we say that the mean is not a resistant measure of center.)
* Calculation and Notation of the mean
* The definition of the mean can be expressed as Formula 3-1, in which the Greek letter ∑ (uppercase sigma) indicates that the data values should be added, so ∑x represents the sum of all data values. The symbol n denotes the sample size, which is the number of data values.
* Mean = ∑xn = <---sum of all data values<---number of data values
* If the data are a sample from a population, the...