# CLT: Question 3

In what way does the sampling distribution of means for a sample with N = 5 differ from a sampling distribution for a sample with N = 100? How do these sampling distributions compare to the population distribution?

#### There is more variance in the sampling distribution with N = 5 than when N = 100, and both sampling distributions have more variance than the population.

There is more variance in the sampling distribution with an N of 5 than an N of 100, but how does the variance of each sampling distribution compare to that of the population? Open the SDM applet and compare the spread in the population distribution (blue) with the spread in the sampling distributions for samples of N = 5 and N = 100 (green).

#### There is less variance in the sampling distribution with N = 5 than when N = 100, and the sampling distribution with N = 100 has a variance similar to the population.

Open the SDM applet and compare the variance found in the respective sampling distributions (in green) of the two different sample sizes. Also compare the spread in the sampling distribution with the spread in the population distribution (blue).

#### The variance is much smaller for the N = 100 sampling distribution than for the N = 5, and both sampling distributions have less variance than the population.

You’re right! We can use the formula from the Central Limit Theorem to show that the sampling distribution with N = 100 has less variance (dispersion) than the sampling distribution with N = 5, and both sampling distributions have lessvariance than the population.