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### Course: Digital SAT Math > Unit 3

Lesson 9: Data inferences: foundations# Data inferences | Lesson

A guide to data inferences on the digital SAT

## What are data inferences questions?

When we want to answer questions like "how many voters feel positively about a new law" or "what percentage of Americans exercise regularly", it's often impractical to ask everyone—it would take a lot of time and effort to ask every voter, let alone every American!

Instead, when we have questions about a large

**population**, we often answer those questions by surveying a**representative sample**: a smaller set of people whose answers can give us a good idea of how the population would answer the same questions. In this lesson, we'll learn to:

- Make generalizations about a population based on sampling data
- Use margin of error to describe the uncertainty of sampling

**You can learn anything. Let's do this!**

## How do I make generalizations about a population using sampling data?

### Estimating using sample proportions

A

**random sample**drawn from a population is representative of the population. With a representative sample, we can multiply the by the population to get an estimate.#### Let's look at some examples!

A representative sample of households in City A reveals that $14.8\mathrm{\%}$ of the households in the sample have exactly two children under the age of $18$ . If City A has a total of $\mathrm{59,317}$ households, approximately how many of them have exactly two children under the age of $18$ ?

### Try it!

## What is margin of error?

While we can make reasonable estimates using sample proportions, we can never be $100\mathrm{\%}$ certain that the population proportion matches the sample proportion

*exactly*. Margins of error let us address the uncertainty inherent to sampling.The margin of error is most commonly given as a percentage. When given a percent estimate and a margin of error, we can establish a range around the estimate by adding and subtracting the margin of error.

For example, if a poll estimates that a political candidate will win $51\mathrm{\%}$ of the popular vote with a margin of error of $2\mathrm{\%}$ , what it actually means is that the poll is reasonably sure that the candidate will actually win $51\mathrm{\%}\pm 2\mathrm{\%}$ of the popular vote, or anywhere between $49\mathrm{\%}$ and $53\mathrm{\%}$ .

**Note:**in the above example, there's still no

The larger a sample size is, the smaller the margin of error will be. Think about it this way: if we want to make an estimate about a population of a million people, we'll get a more accurate result if we ask a random sample of $5000$ people than if we ask only a random sample of $50$ .

### Try it!

## Your turn!

## Things to remember

The larger a sample size is, the smaller the margin of error will be.

## Want to join the conversation?

- I feel like this all feels too easy when you're practicing but when you give the actual test ,the score is always underwhelming(94 votes)
- but this is because you didn't studied or because the exercises are too lower level compared to the questions of the test?(10 votes)

- I finished this lesson in 14±2 minutes(37 votes)
- It seems SAT Math is easy than our A levels(14 votes)
- Yes, honestly, I'm studying for my Nigerian JAMB exams and SAT math is by far easier and less broad than JAMB or even my school A Level Math.(10 votes)

- Will we be always given the margin of error on the SAT or will we ever have to calculate it?(5 votes)
- I always see your comments on the videos/articles. Have you finished the DSAT math and/or reading course? If so, has it helped you improve your score?(3 votes)

- I completed this lesson in 9 ± 3 minutes(5 votes)
- how to calculate the margin of error if asked in the test?(5 votes)
- It means Plus or Minus. 2±1 could equal both 2+1=3 and 2-1=1(8 votes)

- where do i find video about probability(1 vote)
- On youtube there is a playlist which consicy of +40 videos about basics of probability,all these videos were filmed by Khan Academy and the voice actor there is Sal.(5 votes)

- The best part of this section is getting the answer by simple multiplication, subtraction, and addition. You could do it in your mind lol.(3 votes)
- For those who solved practice test 2 (digital), did you find it easier or harder than practice test 1?(3 votes)