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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 and 18 are women, then the proportion of men students is and the proportion of women students is . Mean and proportion are discussed in more detail in later chapters.
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."
Determine what the key terms refer to in the following study. We want to know the average (mean) amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly survey 100 first year students at the college. Three of those students spent $150, $200, and $225, respectively.
The population is all first year students attending ABC College this term.
The sample could be all students enrolled in one section of a beginning statistics course at ABC College (although this sample may not represent the entire population).
The parameter is the average (mean) amount of money spent (excluding books) by first year college students at ABC College this term.
The statistic is the average (mean) amount of money spent (excluding books) by first year college students in the sample.
The variable could be the amount of money spent (excluding books) by one first year student. Let X = the amount of money spent (excluding books) by one first year student attending ABC College.
The data are the dollar amounts spent by the first year students. Examples of the data are $150, $200, and $225.
Determine what the key terms refer to in the following study. We want to know the average (mean) amount of money spent on school uniforms each year by families with children at Knoll Academy. We randomly survey 100 families with children in the school. Three of the families spent $65, $75, and $95, respectively.
The population is all families with children attending Knoll Academy.
The sample is a random selection of 100 families with children attending Knoll Academy.
The parameter is the average (mean) amount of money spent on school uniforms by families with children at Knoll Academy.
The statistic is the average (mean) amount of money spent on school uniforms by families in the sample.
The variable is the amount of money spent by one family. Let X = the amount of money spent on school uniforms by one family with children attending Knoll Academy.
The data are the dollar amounts spent by the families. Examples of the data are $65, $75, and $95.
Determine what the key terms refer to in the following study.
A study was conducted at a local college to analyze the average cumulative GPA’s of students who graduated last year. Fill in the letter of the phrase that best describes each of the items below.
1._____ Population 2._____ Statistic 3._____ Parameter 4._____ Sample 5._____ Variable 6._____ Data
Determine what the key terms refer to in the following study.
As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies. Here is the criterion they used:
| Speed at which Cars Crashed | Location of “drive” (i.e. dummies) |
| 35 miles/hour | Front Seat |
Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.
The population is all cars containing dummies in the front seat.
The sample is the 75 cars, selected by a simple random sample.
The parameter is the proportion of driver dummies (if they had been real people) who would have suffered head injuries in the population.
The statistic is proportion of driver dummies (if they had been real people) who would have suffered head injuries in the sample.
The variable X = the number of driver dummies (if they had been real people) who would have suffered head injuries.
The data are either: yes, had head injury, or no, did not.
Determine what the key terms refer to in the following study.
An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.
The population is all medical doctors listed in the professional directory.
The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in the population.
The sample is the 500 doctors selected at random from the professional directory.
The statistic is the proportion of medical doctors who have been involved in one or more malpractice suits in the sample.
The variable X = the number of medical doctors who have been involved in one or more malpractice suits.
The data are either: yes, was involved in one or more malpractice lawsuits, or no, was not.
Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average (mean) number of glasses of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.
The Data and Story Library, http://lib.stat.cmu.edu/DASL/Stories/CrashTestDummies.html (accessed May 1, 2013).
The mathematical theory of statistics is easier to learn when you know the language. This module presents important terms that will be used throughout the text.
Use the following information to answer the next five exercises. Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once they start the treatment. Two researchers each follow a different set of 40 patients with AIDS from the start of treatment until their deaths. The following data (in months) are collected.
Determine what the key terms refer to in the example for Researcher A.
parameter
The average length of time (in months) AIDS patients live after treatment.
statistic
variable
X = the length of time (in months) AIDS patients live after treatment
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