Nearly every dataset in this course arrives the same way. It's a table, one row per thing observed, one column per fact recorded about it. Reading that layout fluently means knowing which direction is an observation and which direction is a variable. It's a small skill. It pays off on the very first page of the next chapter.
Read a table the way you'd read a class roster. Each row is one student's whole record. Each column is one fact, like grade, age, or GPA, repeated once per student down the page. Scanning down a column compares the same fact across everyone. Scanning across a row reads everything known about one person.
In a data table, each row is one observation: one person, one unit, one trial. Each column is one variable: one measured or recorded fact about every observation. A table with 30 rows and 5 columns records 5 facts about each of 30 observations. It does not record 30 facts about 5 things. That mix-up is easy to make when you read a table sideways.
Find the rows that match a condition
Each chip is one respondent's record: age, class year. Click every respondent who is a sophomore.
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Worked example
Rows vs. columns
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A table has columns Name, Age, GPA and 40 rows. How many observations and how many variables does it record?
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Rows are observations; columns (other than a name/ID label) are variables. 40 rows means 40 observations; Age and GPA are 2 recorded variables.
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3\boxed{40 \text{ observations}, \ 2 \text{ variables (Age, GPA)}}
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Worked example
A misread table
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A student says a table with 5 columns and 200 rows "has 5 observations." What went wrong, and what's the correct read?
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The student swapped rows and columns. Each of the 200 rows is one observation; the 5 columns are the variables recorded about each one.
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3\boxed{200 \text{ observations}, \ 5 \text{ variables} - \text{not the reverse}}
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Where this goes next
Chapter 01, the data matrix
The next chapter names this layout the data matrix. It then builds a whole vocabulary on top of "rows are observations, columns are variables." That vocabulary sorts variables by type. It covers qualitative versus quantitative. It covers discrete versus continuous. It covers levels of measurement, too. Getting the direction right here keeps that sorting from coming out backwards.
Check your understanding (counts toward your progress)
Scanning DOWN a single column of a data table lets you compare:
Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.
That's scanning ACROSS a row, not down a column.
Why
A column holds one variable's values, one per row — reading down it compares that single fact across every observation.
A classmate says a table with 5 columns 'has 5 observations.' Explain their mistake.
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Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.
First mistake
Correct answer
Also accepted:
Why
Why
Columns are variables, not observations — the classmate swapped rows and columns. The number of observations is the number of ROWS; columns just count how many facts are recorded about each one.
A data table has 6 columns and 150 rows. How many observations does it record?
Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.
6 is the number of VARIABLES (columns), not observations.
150/6 isn't a meaningful quantity here.
6 × 150 counts every cell in the table, not the number of observations.
Why
Each row is one observation, so 150 rows means 150 observations, regardless of how many columns (variables) are recorded about each.