Getting a Handle on Bias, Variables, and the Mean
As you work with statistics, you will encounter some vocabulary terms, such as bias, variables, and the mean that you’ll need to understand to answer problems. As soon as you understand what the language means, you immediately will start feeling more comfortable.

Bias is systematic favoritism in the data.

A variable is a characteristic or measurement on which data is collected and whose result can change from one individual to the next.

The mean is the average.
Sample questions
You’re interested in the percentage of female versus male shoppers at a department store. So one Saturday morning, you place data collectors at each of the store’s four entrances for three hours, and you have them record how many men and women enter the store during that time.

Why can collecting data at the store on one Saturday morning for three hours cause bias in the data?
(A) It assumes that Saturday shoppers represent the whole population of people who shop at the store during the week.
(B) It assumes that the same percentage of female shoppers shop on Saturday mornings as any other time or day of the week.
(C) Perhaps couples are more likely to shop together on Saturday mornings than during the rest of the week, bringing the percentage of males and females closer than during other times of the week.
(D) The subjects in the study weren’t selected at random.
(E) All of these choices are true.
Answer: E. All of these choices are true.
You want to get data that represents all customers at the store, no matter what day or what time they shop, whether they shop in couples or alone, and so on. You can’t assume that the people who shopped during those three hours on that Saturday morning are representative of the store’s total clientele. Therefore, this sample wasn’t drawn randomly.

Because a variable is a characteristic of each individual on which data is collected, which of the following are variables in this study?
(A) the day you chose to collect data
(B) the store you chose to observe
(C) the gender of each shopper who comes in during the time period
(D) the number of men entering the store during the time period
(E) Choices (C) and (D)
Answer: E. Choices (C) and (D) (the gender of each shopper who comes in during the time period; the number of men entering the store during the time period)
Gender is a variable, and the number of men entering the store is also a variable. The day you collect data and the store you observe are just part of the design of your study and were determined beforehand.

In this study, _____ is a categorical variable, and _____ is a quantitative variable.
Answer: gender; number of shoppers
Gender is a categorical variable (the categories are male or female), and number of shoppers is a quantitative variable (because it represents a count). The day you collect data and the store you observe are just part of the design of your study and were determined beforehand.

Which chart or graph would be appropriate to display the proportion of males versus females among the shoppers?
(A) a bar graph
(B) a time plot
(C) a pie chart
(D) Choices (A) and (C)
(E) Choices (A), (B), and (C)
Answer: D. Choices (A) and (C) (a bar graph; a pie chart)
Gender is a categorical variable, so both bar graphs and pie charts are appropriate to display the proportion of males versus females among the shoppers. You could use a time plot only if you knew how many males and how many females were in the store at each individual time period.
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