CENTRAL LIMIT THEOREM

Front

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 shape of the population distribution.

Front

What is the standard deviation of a population?

Back

The standard deviation of a population is a measure of the amount of variation or dispersion in a set of values, calculated as the square root of the variance.

Front

What is the mean of a sampling distribution?

Back

The mean of a sampling distribution is equal to the mean of the population from which the samples are drawn.

Front

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

Back

The standard error of the mean (SEM) is calculated as SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

Front

Why is random sampling important?

Back

Random sampling is important because it helps to reduce bias and ensures that every member of the population has an equal chance of being selected.

Front

What does a normal distribution look like?

Back

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

Front

What is the significance of the 68-95-99.7 rule?

Back

The 68-95-99.7 rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

How does sample size affect the Central Limit Theorem?

Back

As the sample size increases, the sampling distribution of the sample mean becomes more normally distributed, regardless of the population's distribution.

Front

What is the difference between a population and a sample?

Back

A population includes all members of a specified group, while a sample is a subset of the population used to represent the whole.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of the distribution.