Central Limit Theorem

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What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Front

What is the mean in statistics?

Back

The mean is the average of a set of numbers, calculated by adding all the values together and dividing by the number of values.

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What is the standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

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What does it mean for a distribution to be normal?

Back

A normal distribution is a symmetric, bell-shaped distribution where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

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How does sample size affect the Central Limit Theorem?

Back

As the sample size increases, the distribution of the sample means becomes more normal, even if the original population distribution is not normal.

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What is the formula for calculating the standard error of the mean?

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Standard Error (SE) = Standard Deviation (σ) / √n, where n is the sample size.

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What is the significance of the 30-sample size rule in the Central Limit Theorem?

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A sample size of 30 is often considered sufficient for the Central Limit Theorem to hold, meaning the sample means will be approximately normally distributed.

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What is a sampling distribution?

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A sampling distribution is the probability distribution of a statistic (like the mean) obtained from a large number of samples drawn from a specific population.

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When should you use the normal distribution instead of the Central Limit Theorem?

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Use the normal distribution when the population is normally distributed or when the sample size is large enough for the Central Limit Theorem to apply.

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What is the probability of a sample mean falling within a certain range?

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To find the probability of a sample mean falling within a certain range, you can use the Z-score formula and standard normal distribution tables.