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## SAT

### Course: SAT > Unit 6

Lesson 5: Problem Solving and Data Analysis: lessons by skill- Ratios, rates, and proportions | Lesson
- Percents | Lesson
- Units | Lesson
- Table data | Lesson
- Scatterplots | Lesson
- Key features of graphs | Lesson
- Linear and exponential growth | Lesson
- Data inferences | Lesson
- Center, spread, and shape of distributions | Lesson
- Data collection and conclusions | Lesson

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# Table data | Lesson

## 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 concert | Did not attend concert | Total | |
---|---|---|---|

Dr. Romelle's class | 17 | 14 | 31 |

Dr. Yukevich's class | 23 | 10 | 33 |

Total | 40 | 24 | 64 |

In this lesson, we'll learn to:

- Read two-way frequency tables
- Use two-way frequency tables to calculate proportions and probabilities
- 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 concert | Did not attend concert | Total | |
---|---|---|---|

Dr. Romelle's class | 17 | 14 | 31 |

Dr. Yukevich's class | 23 | 10 | 33 |

Total | 40 | 24 | 64 |

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!

## 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 concert | Did not attend concert | Total | |
---|---|---|---|

Dr. Romelle's class | 17 | 14 | 31 |

Dr. Yukevich's class | 23 | 10 | 33 |

Total | 40 | 24 | 64 |

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!

## 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 instrument | Does not play an instrument | Total | |
---|---|---|---|

Dr. Romelle's class | 20 | 11 | 31 |

Dr. Yukevich's class | 33 | ||

Total | 64 |

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!

## Your turn!

## Want to join the conversation?

- On the last question, why did they multiply 3 by 2?(3 votes)
- 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)

- 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)- 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)