Sampling Distributions - Means

Front

What is a sampling distribution?

Back

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.

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, regardless of the population's distribution.

Front

What is the mean of a sampling distribution of sample means?

Back

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

Tags

CCSS.6.SP.A.2

Front

What is the standard deviation of a sampling distribution called?

Back

The standard deviation of a sampling distribution is called the standard error.

Front

How do you calculate the standard error?

Back

The standard error (SE) is calculated as the population standard deviation (σ) divided by the square root of the sample size (n): SE = σ/√n.

Front

What is the relationship between sample size and standard error?

Back

As the sample size increases, the standard error decreases, leading to a more precise estimate of the population mean.

Front

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.

Front

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

Back

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.

Tags

CCSS.HSS.ID.A.4

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It is calculated as Z = (X - μ) / σ.

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, and 99.7% within three.

Tags

CCSS.HSS.ID.A.4