How does sample size affect variance

As a sample size increases, sample variance (variation between observations) increases but the variance of the sample mean (standard error) decreases and hence precision increases.

1. How does sample size affect variation?
2. Why does increasing sample size decrease variance?
3. Why does variance increase when sample size increases?
4. How does sample size affect bias and variance?

How does sample size affect variation?

There is an inverse relationship between sample size and standard error. In other words, as the sample size increases, the variability of sampling distribution decreases.

Why does increasing sample size decrease variance?

As the sample size increases the sampling distribution tends to become normal. That is the sampling distribution becomes leptokurtic in nature. It happens only because with the increasing sample size the variability decreases as the sampling distribution resembles the population to a great extent.

Why does variance increase when sample size increases?

The mean of the sample means would be very close to μ, the mean for the population from which the samples were drawn. However, the variability in the sample means will depend on the size of the samples, since larger samples are more likely to give estimated means that are closer to the true mean of the population.

How does sample size affect bias and variance?

The size of the bias is proportional to population variance, and it will decrease as the sample size gets larger.