One of the main concerns in the field of statistics

One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The accuracy really
depends on how well the sample represents the population. The sample must contain the characteristics of the population
in order to be a representative sample . We are interested in both the sample statistic and the population parameter in
inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population
parameter.
A variable , or random variable, notated by capital letters such as X and Y , is a characteristic of interest for each person or
thing in a population. Variables may be numerical or categorical . Numerical variables take on values with equal units
such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. If we let X
equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be
a person's party affiliation, then some examples of Y include Republican, Democrat, and Independent. Y is a categorical
variable. We could do some math with values of X (calculate the average number of points earned, for example), but it
makes no sense to do math with values of Y (calculating an average party affiliation makes no sense).
Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.
Two words that come up often in statistics are mean and proportion . If you were to take three exams in your math classes
and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by
three (your mean score would be 84.3 to one decimal place). If, in your math class, there are 40 students and 22 are men
4 Chapter 1 | Sampling and Data
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and 18 are women, then the proportion of men students is
22
40
and the proportion of women students is
18
40
. Mean and
proportion are discussed in more detail in later chapters.
NOTE
The words " mean " and " average " are often used interchangeably. The substitution of one word for the other is
common practice. The technical term is "arithmetic mean," and "average" is technically a center location. However, in
practice among non-statisticians, "average" is commonly accepted for "arithmetic mean."