AP Statistics – Data, Variables, & Other Vocabulary

  1. Write in one, grammatically correct sentence explaining your primary reason for taking this course.
  1. For each word in response to question 1, record the number of letters in the word:

The numbers that you have recorded are data. Not all numbers are data, however, Data are numbers collected in a particular context. For example, the numbers 3 and 7, 35 and 19 do not constitute data in and of themselves. They are data, however, if they refer to the number of letters in the first two words of your response to question 1 or the number of states visited by two of the students in this class.

  1. Did every word that you wrote contain the same number of letters?

The answer to this obvious question reveals the most fundamental principle of statistics: variability. Data vary, and variability abounds both in everyday life and in academic study. The students in this class vary with respect to gender, length of signature, number of states visited, and lots of other variables.

A variable is any characteristic of a person or thing to which the number or category that can be assigned a number or category. The person or thing, to which the number or category is assigned, such as student in your class, is called the observational unit or case. A quantitative or measurement variable is typically one that measures a numerical characteristic, while a categorical or qualitative variable is one that simply records a category designation. Binary variables are categorical variables for which only two possible categories exist. These designations can be quite important, for one typically employs different statistical tools depending on the type of variable measured.

Consider the students in your class as observational units.

  1. Which of the following are legitimate variables that can be measured on those observational units? [Hint: Ask yourself whether the value can change from observational unit to observational unit.] For each that is a variable, indicate whether it is a quantitative or a categorical variable. If it is a categorical variable, indicate whether or not it is a binary variable.

·  Hair color:

·  Number of student with red hair:

·  Height of tallest student in your class:

·  Whether or not a student has red hair:

·  Height:

·  Instructor’s age:

·  Zip code of home town:

  1. If the observational units had been classes at your school, would “number of students in the class with red hair” be a variable? Explain.

As the term “variable” suggests, the values assumed by a variable can differ from observational unit to observational unit. For example hair color differs from person to person, and whether or not a student has red hair differs as well. However, the number of students with red hair in your class summarizes the variable for all students in your class and so does not vary from student to student.

  1. The observation units for the variables listed below are students in your class. For each variable, indicate whether it is a quantitative or a categorical (qualitative) variable. If it is a categorical variable, indicate whether or not it is binary variable.

·  Gender:

·  Length of signature:

·  Number of states visited:

·  Political identification:

  1. What are the observational units for the “letters per word” variable on which you recorded data in question 1 & 2?
  1. Suppose that instead of recording the number of letters in each word of your sentence, you had been asked to classify each word according to the following criteria:
  2. 1 – 3 letters: small word
  3. 4 – 6 letters: medium word
  4. 7 – 9 letters: big word
  5. 10 or more letters: very big word

In this case, what type of variable is “size of word”?

  1. Considering the states as the observational units, what type of variable is “whether or not you have visited a particular state”?
  1. In 1998, the American Film Institute selected the 100 best films of all time. The following variables use these films as observational units. Identify the type of each of the following variables.
  1. year produced
  2. number of years since production
  3. decade produced
  4. whether or not it was produced before 1960
  5. whether it won an Academy Award for Best Picture
  6. whether or not you have seen it
  7. the number of people in your class who have seen it

AP Statistics – Observational Units, Variables, Parameters and statistics

  1. Lambert and Pinheiro (2006) describe a study in which researchers try to identify characteristics of cell phone calls that suggest the phone is being used fraudulently. For each cell phone call, the researchers recorded information on its direction (incoming or outgoing), location (local or roaming), duration, time of day, day of week, and whether the call took place on a weekday or weekend.
  2. Identity the observational units in this study.
  3. Identify the categorical variables mentioned in the preceding paragraph. Indicate which are binary and which are not.
  4. Identify the quantitative variables mentioned in the preceding paragraph.
  1. Statistical evidence played an important role in the murder trial of Kristen Gilbert, a nurse who was accused of murdering hospital patients by giving them fatal doses of a heart stimulant (Cobb and Gerlach, 2006). Hospital records for an eighteen-month period indicated that of the 257 eight-hour shifts that Gi9lbert worked, a patient died on 40 of those shifts (15.6%). But during the 1384 eight-hour shifts that Gilbert did not work, a patient died on only 34 of those shifts (2.5%).
  2. Identify the observational units in this study. Hint: The correct answer here is more subtle than most students expect.
  3. Identify the two variables mentioned in the preceding paragraph. Classify each a categorical (possibly binary) or quantitative.
  1. Suppose that you are given a sample of 25 Reese’s Pieces candies and asked to record the color of each candy.
  2. What are the observational units?
  3. What is the variable? Is it categorical (also binary) or quantitative?
  1. Now suppose that your classmates are each given a sample of 25 Reese’s Pieces candies. Also suppose that students are asked to report the proportion of orange candies in their sample of 25 candies.
  2. Now what are the observational units?
  3. Now what is the variable? Is it categorical (also binary) or quantitative?
  1. Consider the student in your class as a sample from the population of all students at your school. Identify each of the following as a parameter or a statistics:
  2. The proportion of students in your class who use instant-messaging or text-messaging on a daily basis.
  3. The proportion of students at your school who use instant-messaging or text-messaging on a daily basis.
  4. The average number of hours students at your school spent watching television last week.
  5. The average number of hours student in your class slept last night.
  1. Identify each of the following as a parameter or statistic. If you need to make an assumption about whom or what the population of interest is in a given case explain that.
  2. The proportion of voters who voted for President Bush in the 2004 election.
  3. The proportion of voters surveyed by CNN who voted for John Kerry in the 2004 election.
  4. The proportion of voters among your school’s faculty members who voted for Ralph Nader in the 2004 election.
  5. The average number of points scored in a Super Bowl game.
  6. An article published in the June 6, 2006 issued of the journal Pediatrics describes the results of a survey on the topic of college students injuring themselves intentionally (Whitlock, Eckenrode, and Silverman, 2006). Researches invited 8300 undergraduate and graduate students at Cornell University and Princeton University to participate in the survey. A total of 2875 students responded, with 17% of them saying that they had purposefully injured themselves.
  7. Identify the observational units and a variable in this study. Also, classify the variable as categorical (also binary) or quantitative.
  8. Identify the population and sample.
  9. What is the sample size in this study?
  10. Is 17% a parameter or a statistic? Explain.
  1. For each description of data, identify the W’s, name the variables, specify for each variable whether it use indicates it should be treated as categorical or quantitative, and for any quantitative v arable, identify the units in which it was measured (or note that they were not provided).
  2. According to an article in Fortune(Dec. 29, 1992), 401 k plans permit employees to shift part of their before-tax salaries into investments such as mutual funds. Employers typically match 50% of the employees’ contribution up to 6% of salary. One company, concerned with what it believed was a low employee participation rate in its 401k plan, sampled 30 other companies with similar plans and asked for their 401k participation rates.
  3. Because of the difficulty of weighing a bear in the woods, researchers caught and measured 54 bears, recording their weight, neck size, length and sex. They hoped to find a way to estimate weight from the other, more easily determined quantities.
  4. A listing posted by the Arby’s restaurant chain gives, for each of the sandwiches it sells, the type of meat in the sandwich, the number of calories, and the serving size in ounces. The data might be used to assess the nutritional value of the different sandwiches.