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Course: Digital SAT Math > Unit 11
Lesson 9: Data inferences: advancedData 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 of the households in the sample have exactly two children under the age of . If City A has a total of households, approximately how many of them have exactly two children under the age of ?
Try it!
What is margin of error?
While we can make reasonable estimates using sample proportions, we can never be 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 of the popular vote with a margin of error of , what it actually means is that the poll is reasonably sure that the candidate will actually win of the popular vote, or anywhere between and .
Note: in the above example, there's still no certainty that the candidate will win between to of the popular vote! However, the poll can be more confident in the estimate than in the exact estimate.
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 people than if we ask only a random sample of .
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(87 votes)
- but this is because you didn't studied or because the exercises are too lower level compared to the questions of the test?(8 votes)
- I finished this lesson in 14±2 minutes(21 votes)
- It seems SAT Math is easy than our A levels(11 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.(8 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)
- 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)
- I completed this lesson in 9 ± 3 minutes(4 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)