Read the Study Description for Variables
In Matching Variable Type to the Right Graph or Summary, you practiced choosing a display after identifying a variable and its type. Now you will practice the step that comes first: reading a study description and finding every variable it says was recorded. Study descriptions often mention the participants, setting, procedure, and several measurements in the same paragraph. The challenge is to sort out which details are variables and classify each correctly.
As you learned in What Is a Variable in Statistics and Identifying the Observational Unit, start by asking what one case describes. Then ask which characteristics or measurements were recorded for each case. A variable is not limited to something named in a formal list: it may be embedded in a phrase such as “how many days,” “which category,” or “how long.”
A reliable reading routine is to move through the paragraph in order. First identify who or what is being described. Next underline words and phrases that tell you what was recorded about each unit. For each candidate, ask: could its value differ from one unit to another? If so, it may be a variable. Finally, classify its values by meaning, not by appearance.
Some details describe the study but are not variables. For example, “all participants completed the survey in the library” gives a setting, not a characteristic recorded separately for each participant. A detail that is the same for everyone in the study cannot describe variation among those units in that data set. Similarly, the number of participants is usually the size of the data set, not a variable recorded for each participant.
However, do not leave out a characteristic just because it seems secondary. If the description says researchers recorded each student’s grade level, that is a variable even if the study’s main question concerns sleep. If it says each person received an identification code, the code is a recorded field, though it does not measure an amount. The inventory should make clear what was recorded and what the values mean.
Classify Each Variable by Meaning
Use the distinctions from Categorical Versus Quantitative Variables and Discrete Versus Continuous Quantitative Variables. A categorical variable sorts units into groups. A quantitative variable records a count or measurement for which numerical differences have meaning. For quantitative variables, note whether the values are separate counts or measurements along a continuum.
Some categorical variables have an order. In Ordinal Categories and Rating Scales, you learned that ordered categories can be ranked, but the gaps between neighboring categories are not established as equal. Thus, a rating of “low,” “medium,” or “high” is categorical and ordinal, not a quantitative measurement just because the categories have an order.
Also use the arithmetic-meaning test from Spotting Numerical Variables That Are Really Categorical. A student number, room number, or code can consist of digits without measuring an amount. If subtracting two values does not produce a meaningful difference in the characteristic, the variable is categorical or an identifier—not quantitative.
A good inventory names the variable precisely enough that a reader can tell what one value means. “Sleep” is vague; “hours of sleep reported for the night before the survey” identifies what was recorded and when. “Attendance” could mean a category or a count; “number of school days absent during September” is specific and clearly quantitative.
Worked Example: Sleep and Caffeine Survey
A school nurse invites 32 students to complete a survey on a Monday morning. For each student, the nurse records the student’s grade level, the number of hours slept the previous night, the number of caffeinated drinks consumed the previous day, and whether the student reports feeling rested (“yes” or “no”). Identify the observational units and every variable, then classify each variable.
Identify the units: Each observational unit is one student who completed the survey. The 32 students are the cases described by the data.
Find the recorded characteristics: The paragraph says the nurse records four pieces of information for each student: grade level, hours of sleep, number of caffeinated drinks, and whether the student feels rested. Monday morning is the survey setting, and 32 is the number of participating students; neither is a separate variable recorded about each student in this description.
| Variable | What a value represents | Type | Reason |
|---|---|---|---|
| Grade level | The student’s grade in school | Categorical, ordinal | Grade levels are groups with a meaningful order; the differences between grades are not being measured as an amount here. |
| Hours of sleep | Hours slept the previous night | Quantitative, continuous | Time is a measurement and may include fractions of an hour. |
| Number of caffeinated drinks | Count consumed the previous day | Quantitative, discrete | This is a count of whole drinks. |
| Feeling rested | Yes or no response | Categorical | The values name two groups rather than amounts. |
Check completeness: There are four recorded characteristics in the description, and all four appear in the inventory. The time reference matters: sleep is for the previous night, while the drink count is for the previous day. Including those details makes the variable names precise and keeps them distinct from other possible sleep or caffeine measures.
Interpret the inventory: This data set has 32 student cases and four variables. Two variables are categorical and two are quantitative. Grade level is an ordered category; do not treat it as a measurement of an amount merely because grades can be written with numbers.
Separate Variables from Other Study Details
A paragraph may mention facts that are important to understanding how a study was conducted without making them variables in the recorded data. The setting, dates, instructions, or a procedure may be constant for all cases. Those details belong in a description of the study, but they do not belong in the variable inventory unless the study records a value for each unit.
A useful test is to complete the sentence “For each student, the researchers recorded ___.” If the paragraph supports filling the blank with a characteristic or measurement, include it. If it only says where the study happened or how all participants were instructed, it is probably a study detail. Do not invent unmentioned variables based on what researchers might have collected.
Sometimes the same kind of fact can be either a variable or a study detail depending on the wording. “The students were surveyed in the school gym” gives one shared setting. “For each student, researchers recorded whether the survey was completed in the gym or library” describes a categorical variable. Look for evidence that a value was recorded for each case.
A recorded identifier deserves special care. In Reading a Data Table: Rows, Columns, and Cases, you learned that columns can contain variables. An ID column may indeed vary from row to row, but its values identify cases rather than describe a measured characteristic. Mention it when listing recorded fields, and label it as an identifier so no one mistakes it for a quantitative measurement or an interesting category to summarize.
Worked Example: Attendance and School Belonging
A counselor surveys 40 students from two middle schools. For each student, the counselor records a student code, the school attended, the number of days absent during the current term, and a response to “How connected do you feel to your school?” on a scale of “not at all,” “a little,” “somewhat,” and “very.” All surveys are completed during advisory period. Identify the units and all recorded fields, and classify each field appropriately.
Identify the units: One observational unit is one surveyed student. There are 40 student cases.
Extract the fields: The paragraph explicitly says that four items are recorded for each student: student code, school attended, number of days absent, and connectedness rating. Advisory period is the shared survey time, not a recorded variable here.
| Recorded field | Classification | Explanation |
|---|---|---|
| Student code | Identifier; categorical label | It distinguishes students but does not measure an amount. Differences between codes have no meaningful interpretation. |
| School attended | Categorical | Each value names one of the two schools. |
| Days absent during the term | Quantitative, discrete | It is a count of days, so values are separate whole-number counts. |
| Connectedness rating | Categorical, ordinal | The four response categories have a natural order, but equal gaps between them have not been established. |
Check the boundaries: “Two middle schools” describes the setting and gives context; because school attended is recorded for each student, that characteristic is also a variable. “All surveys are completed during advisory period” is only a shared procedure in this description. It is not a variable because no different time value is recorded for each student.
Interpret the inventory: The study has four recorded fields, including an identifier. Three fields describe student characteristics or responses, and the code identifies the cases. Of the three descriptive variables, school attended is categorical, days absent is quantitative and discrete, and connectedness is ordinal categorical. The code’s digits should not be averaged or displayed on a quantitative scale.
A Repeatable Inventory Method
When a study description is long, build the inventory in two passes. On the first pass, mark every phrase that appears to describe something recorded for each unit. On the second pass, turn each phrase into a clear variable name and classify it. Then scan the paragraph again for fields you might have missed, especially demographic details, counts, ratings, and identifiers.
Ask what one case represents: one student, patient, school, appointment, or other individual.
Look for wording such as “for each,” “records,” “measures,” “asks,” or “reports.” Include each characteristic with a value for a case.
Distinguish per-case information from shared study details such as a common location or procedure. Do not add information that the paragraph does not say was recorded.
Decide whether values are categories or meaningful amounts. Note ordered categories, discrete counts, continuous measurements, and numerical labels.
Confirm that each recorded field appears once, each variable name says what was recorded, and no study detail has been mistaken for a variable.
Worked Example: A School Reading Check-In
A teacher asks 28 students to keep a one-week reading log. For each student, the teacher records the student’s homeroom, the total number of minutes spent reading during the week, the number of days on which the student read, and the student’s answer to whether the log was easy to use (“yes” or “no”). The class uses the same log sheet. Identify the units and every recorded variable, and classify them.
Identify the units: One observational unit is one student who completed the reading log. The data describe 28 students.
Extract the recorded variables: The per-student fields are homeroom, total reading minutes, days read, and ease-of-use response. The shared log sheet is part of the procedure, not a variable, because the description does not say that different log sheets were recorded for different students.
| Variable | Type | Reason |
|---|---|---|
| Homeroom | Categorical | It identifies a group to which the student belongs. |
| Total reading minutes during the week | Quantitative, continuous | Duration is a measurement; it can be recorded with fractional minutes. |
| Number of days on which the student read | Quantitative, discrete | This is a count of days and takes whole-number values from 0 through 7. |
| Ease-of-use response | Categorical | “Yes” and “no” are response groups, not numerical amounts. |
Check the wording: “Total number of minutes” can sound like a count because it includes the word “number.” But the underlying quantity is time spent reading, which is measured. By contrast, “number of days” counts separate events or occasions. The meaning of the recorded values—not a single word in the sentence—determines the type.
Interpret the inventory: There are four variables for each of the 28 student cases. Two are quantitative and two are categorical. This list would help the teacher choose suitable displays later: for example, the reading minutes and days read are quantitative, while homeroom and the yes-or-no response are categorical.
Common Mistakes and AP Exam Tips
- Stopping after naming the main outcome. A study description may include several recorded characteristics. Scan for every “records,” “asks,” or “measures” phrase and check that each per-case field appears in your inventory.
- Listing the sample size as a variable. “Forty students were surveyed” tells you how many cases there are. It is not ordinarily a value recorded for each student.
- Treating a shared procedure as a variable. A common survey location or instruction is not a variable unless different values are recorded for the individual cases.
- Calling every number quantitative. A code or homeroom number may be a label. Explain what the digits mean before deciding that arithmetic differences are meaningful.
- Calling ordered responses quantitative. “Low,” “medium,” and “high” have an order, but that does not establish equal numerical gaps. Classify them as ordinal categorical.
- Using vague variable names. “Time,” “attendance,” or “rating” may be ambiguous. State what was measured or counted and specify the relevant period or scale when the description provides it.
For a strong AP Statistics response, name the observational units, list every recorded variable, and give a brief reason for each type. For example: “The units are the surveyed students. Days absent is quantitative and discrete because it counts whole days; the four-level belonging response is ordinal categorical because its categories have an order, but equal gaps are not established.” This is more informative than giving type labels alone.
Check Your Understanding
For each study description, name the observational units, list the recorded variables, and classify each variable. State any field that is an identifier or a shared study detail rather than a descriptive variable.
- A clinic records each patient’s age in years, appointment type (routine or follow-up), and number of minutes spent waiting. All patients check in at the same reception desk. What are the units and variables?
- A school surveys students about how often they bring lunch: never, sometimes, or always. It also records each student’s grade and the number of school days they were absent last month. Classify every variable.
- A recreation program records each participant’s badge number, chosen activity, and distance walked in kilometers during one outing. Is the badge number quantitative? Explain.
- A nurse records each child’s temperature and whether the child has a cough. The description says all children were examined on Tuesday. Which details are variables, and how should they be classified?
- A teacher gives every student the same reading instructions, then records the number of pages each student reads and a satisfaction rating of “poor,” “fair,” “good,” or “excellent.” Identify the two variables and classify them.