What is Statistics?
Statistics is the science of reasoning from data, so a natural place to begin your study is by
examining what is meant by the term
data
. You will find that data
vary,
and variability
abounds in everyday life and in academic study. Indeed, the most fundamental principle in
statistics is that of variability. If the world were perfectly predictable and showed no
variability, you would not need to study statistics. Thus, you will learn about variables and
consider their different classifications. You will also begin to experience the interesting
research questions that you can investigate by collecting data and conducting statistical
analyses.
How can statistics be used to help decide the guilt or innocence of a nurse accused of
murdering some of her patients?
If chief executive officers tend to be taller than average, would this convince you that being
tall provides advantages in the business world?
Do some students do worse on standardized tests when they are first asked to indicate their
race than when they are not, perhaps due to negative stereotypes of their academic ability?
Vocabulary Supplemental Exercises Chapter 1
1.
Statistics
is a collection of methods for planning experiments, obtaining data, and then organizing,
summarizing, presenting, analyzing, interpreting and drawing conclusions based on the data.
2. A
population
is the complete collection of all elements (scores, people, measurements, and so on) to be
studied. The collection is complete in the sense that it includes all subjects to be studied.
3. A
sample
is a subcollection of elements selected from a population.
Example: In a study of household incomes in a small town of 1000 households, one might conceivably
obtain the income of every household. However, it is probably very expensive and time consuming to do
this.
Therefore, a better approach would be to obtain the data from a portion of the households (let’s say
125 households). In this scenario, the 1000 households are referred to as the population and the 125
households are referred to as a sample.
4. A
parameter
is a numerical measurement describing some characteristic of a
population
and computed
from all of the population measurements.
5. A
statistic
is a numerical measurement describing some characteristic of a
sample
drawn from the
population.
Example: In the household incomes example from above, the average (mean) income of all 1000
households is a parameter, whereas the average (mean) income of the 125 households is a statistic.
6.
Discrete data
result when the number of possible values is either a finite number or a countable number.
(That is, the number of possible values is 0 or 1 or 2 and so on.)
Example: The numbers of fatal automobile accidents last month in the 10 largest US cities