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SAT

Course: SAT > Unit 6

Lesson 5: Problem Solving and Data Analysis: lessons by skill
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SAT
About the SAT Math Test
Problem Solving and Data Analysis: lessons by skill
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Table data | Lesson

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What are table data problems, and how frequently do they appear on the test?

On the SAT, table data problems ask you to use two-way frequency tables to calculate proportions or probabilities.
Two-way frequency tables include two qualitative variables, one represented by rows and the other represented by columns. For example, the table below summarizes the concert attendance of students in Dr. Romelle and Dr. Yukevich's classes. The two variables are class and concert attendance.
Attended concertDid not attend concertTotal
Dr. Romelle's class171431
Dr. Yukevich's class231033
Total402464
In this lesson, we'll learn to:
  1. Read two-way frequency tables
  2. Use two-way frequency tables to calculate proportions and probabilities
  3. Use proportions and probabilities to find missing values
On your official SAT, you'll likely see 1 question that tests your ability to use two-way frequency tables. Occasionally, you may also need to read two-way frequency tables to identify a value for a multi-step word problem or calculate the center or spread.
You can learn anything. Let's do this!

How do I read two-way frequency tables?

The biggest challenge of table data problems is understanding what the question is asking for. Let's describe some of the values in the table below.
Attended concertDid not attend concertTotal
Dr. Romelle's class171431
Dr. Yukevich's class231033
Total402464
The number 17 is in the row "Dr. Romelle's class" and the column "attended concert". We can make a few similar statements using the number 17:
  • 17 students both attended the concert and are from Dr. Romelle's class.
  • 17 students from Dr. Romelle's class attended the concert.
  • 17 of the students who attended the concert are from Dr. Romelle's class.
The number 40 is the total for the column "attended concert". This means 40 students (from both Dr. Romelle and Dr. Yukevich's classes) attended the concert.
Similarly, the number 33 is the total for the row "Dr. Yukevich's class". This means there are 33 students in Dr. Yukevich's class (some attended the concert, some did not).
The number 64 in the lower right corner is total number of students for all categories.

Try it!

Try: identify values based on their descriptions
Owns a skateboardDoes not own a skateboardTotal
Owns a bike41115
Does not own a bike3710
Total71825
Jackie asked his classmates whether they own a bike or a skateboard. The results are shown in the table above.
How many classmates own both a bike and a skateboard?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
How many classmates own skateboards?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
How many classmates own either a bike or a skateboard, but not both?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

How do I calculate proportions and probabilities using two-way frequency tables?

Once we correctly identify the values we're looking for in a problem, the rest of the problem is basically dividing two values to find a fraction, percentage, or probability.
Note: While proportions and probabilities are different concepts, we perform the same calculations for them in the context of table data problems.
Let's use the table below for some example calculations!
Attended concertDid not attend concertTotal
Dr. Romelle's class171431
Dr. Yukevich's class231033
Total402464
What fraction of Dr. Romelle's class did not attend the concert?
What percent of students from both classes attended the concert?
If a student from both classes is selected at random, what is the probability that the student is from Dr. Yukevich's class and attended the concert?

Try it!

Try: calculate a proportion and a probability
Owns a skateboardDoes not own a skateboardTotal
Owns a bike41115
Does not own a bike3710
Total71825
Jackie asked his classmates whether they own a bike or a skateboard. The results are shown in the table above.
If a classmate is selected at random, what is the probability that they do not own a bike? (Enter your answer as a fraction or decimal between 0 and 1.)
  • Your answer should be
  • a proper fraction, like 1, slash, 2 or 6, slash, 10
  • an exact decimal, like 0, point, 75
What fraction of classmates who do not own a skateboard also do not own a bike? (Enter your answer as a fraction between 0 and 1.)
  • Your answer should be
  • a proper fraction, like 1, slash, 2 or 6, slash, 10

How do I find missing values in a table?

Note: missing value questions appear very rarely on the SAT.
Just as we can calculate a proportion or probability using the values in two-way frequency tables, we can calculate missing values in a table when given a proportion or probability.
Some two-way frequency tables do not provide the totals for us. For these tables, it's helpful to add a row and a column for the totals.
Let's look at another example using the students in Dr. Romelle and Dr. Yukevich's classes.
Plays an instrumentDoes not play an instrumentTotal
Dr. Romelle's class201131
Dr. Yukevich's class33
Total64
If start fraction, 3, divided by, 4, end fraction of the students in the two classes play an instrument, how many students in Dr. Yukevich's class play an instrument?

Try it!

try: find missing values in a table
B or betterC or worse
Finished book81
Did not finish book
The table above shows the grades of 20 students who wrote an essay based on a book. Some of the values are missing.
How many students did not finish the book?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
If 50, percent of the students received a B or better on the essay, how many of those students did not finish the book?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Your turn!

Practice: calculate a probability
Watches gaming livestreamsDoes not watch gaming livestreamsTotal
Plays video games4465109
Does not play video games33942
Total47104151
Barento surveyed 151 high school students on their video game-related activities. The results are summarized in the table above. If one student from the survey is selected at random, what is the probability that the selected student does not play video games and does not watch gaming livestreams?
Choose 1 answer:

Practice: calculate a proportion
Great BritainUnited StatesOther nationsTotal
Gold562331110
Silver511244107
Bronze391256107
Total14647131324
The table above represents the medals won at the 1908 Summer Olympics. Approximately what percent of gold medals were won by Great Britain and the United States?
Choose 1 answer:

Practice: calculate a missing value
Blood Type
Rhesus factorstart text, A, end textstart text, B, end textstart text, A, B, end textstart text, O, end text
plus777619122
minus1x13
Human blood can be classified into four common blood types—start text, A, end text, start text, B, end text, start text, A, B, end text, and start text, O, end text. It is also characterized by the presence left parenthesis, plus, right parenthesis or absence left parenthesis, minus, right parenthesis of the rhesus factor. The table above shows the distribution of blood type and rhesus factor for a group of people. If one of these people who is rhesus negative left parenthesis, minus, right parenthesis is chosen at random, the probability that the person has blood type start text, O, end text is start fraction, 1, divided by, 2, end fraction. What is the value of x ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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  • blobby green style avatar for user Fatima Hisham
    Posted 2 years ago. Direct link to Fatima Hisham's post “On the last question, why...”
    On the last question, why did they multiply 3 by 2?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Hecretary Bird
      Posted 2 years ago. Direct link to Hecretary Bird's post “In this problem, we use w...”
      Good Answer
      In this problem, we use what we know about a table to find a table value. We're looking only at the people that have a negative blood type here, so the bottom row. The chance that someone with a negative rhesus factor has O-type blood is 1/2. Because in the table, 3 people have O- blood, the total group of negative rhesus factor people will be 3 * 2, since the 3 makes up half of the total. Did this answer the question alright?
      (12 votes)
  • blobby green style avatar for user biig quad
    Posted 8 months ago. Direct link to biig quad's post “If a student from both cl...”
    If a student from both classes is selected at random, what is the probability that the student is from Dr. Yukevich's class and attended the concert?

    I felt the answer here's supposed to be
    23/33. Cause,23 out of the whole of Dr. Yukevich's students attended the concert. And the total of all his students are 33. And the question is just so emphatically on Dr. Yukevich,and not Dr. Romelle.
    (0 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Hecretary Bird
      Posted 7 months ago. Direct link to Hecretary Bird's post “You have to be careful ab...”
      You have to be careful about what the probability means here. Selecting a student from both classes at random means that your total would be the combined number of students in both classes, or 64. Then out of those, you want to find the number of students that both attended Dr. Yukevich's class and the concert. To do this, you have to go to the entry in the table that's in Dr. Yukevich's row AND the concert column. We see that this is 23 students, so 23/64 is the probability that a randomly selected student from either class was in Dr. Yukevich's class and attended the concert.
      23/33 would be the probability that someone from Dr. Yukevich's class attended the concert, but the question here wants us to find the probability of a student from both classes. Hope this helps!
      (2 votes)