Central Limit Theorem
Definition
The Central Limit Theorem states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution regardless of the shape of the population distribution.
Analogy
Think about baking cookies. No matter what shape each individual cookie has before baking (some may be misshapen), when you bake a large batch and take an average size from each batch, they tend to resemble more and more like perfectly round cookies due to their collective average.
Related terms
Sampling Distribution: The probability distribution of a statistic obtained through repeated sampling from a population.
Standard Error: An estimate of how much variability exists between sample means when repeatedly taking samples from the same population.
Confidence Interval: A range around an estimated parameter value that is likely to contain the true parameter value with a certain level of confidence.
"Central Limit Theorem" appears in:
Study guides (12)
AP Statistics - 5.3 The Central Limit Theorem
AP Statistics - 5.5 Sampling Distributions for Sample Proportions
AP Statistics - 5.6 Sampling Distributions for Differences in Sample Proportions
AP Statistics - 5.7 Sampling Distributions for Sample Means
AP Statistics - 5.8 Sampling Distributions for Differences in Sample Means
AP Statistics - 7.2 Constructing a Confidence Interval for a Population Mean
AP Statistics - 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval
AP Statistics - 7.4 Setting Up a Test for a Population Mean
AP Statistics - 7.6 Confidence Intervals for the Difference of Two Means
AP Statistics - 7.8 Setting Up a Test for the Difference of Two Population Means
AP Statistics - 9.2 Confidence Intervals for the Slope of a Regression Model
AP Statistics - 9.5 Carrying Out a Test for the Slope of a Regression Model
Additional resources (3)
Practice Questions (17)
- What does the Central Limit Theorem state in the context of constructing confidence intervals?
- According to the Central Limit Theorem, what size does the sample have to be in order for the sampling distribution of the sample mean to be approximately normal?
- For which type of variables is it generally recommended to use the Central Limit Theorem?
- The Central Limit Theorem can be used to calculate probabilities related to which of the following?
- Which of the following criteria does not have to be met in order to use the Central Limit Theorem?
- If a sample size is 20, can we apply the Central Limit Theorem?
- The Central Limit Theorem is applicable to both _ and _ data.
- Which of the following statements about the Central Limit Theorem is true?
- When using the Central Limit Theorem, a _ sample size is _:
- In order to use the Central Limit Theorem, the samples have to be _ of each other.
- Which of the following should you do on the AP Statistics exam in relation to the Central Limit Theorem?
- What does the Central Limit Theorem state about the sampling distribution for the difference in sample proportions?
- What is the "large enough" sample size for Central Limit Theorem?
- What does the Central Limit Theorem state about the sampling distribution of a sample?
- If you were trying to compare the sales of two ice-cream flavors, chocolate and strawberry, and are going to collect a random sample from each, which of the following sample sizes would the Central Limit Theorem not apply to?
- What does the Central Limit Theorem state?
- Which of the following is an assumption for the Central Limit Theorem to apply?
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