## What is the relationship between variances and standard deviations?

Variance refers to the average squared deviations of the mean. Standard deviation is the square root. Both measures measure variability in a distribution. However, their units are different: Standard deviation is expressed using the same units as original values (e.g. minutes or meters).

## Does the standard deviation change if the mean changes?

(a If you multiply each term by the same number, then the SD will change. The SD will also change by the same number. The mean will change by the same amount.

**What is the relationship between sample size and standard deviation? **

Spread – The spread of larger samples is lower, so the standard deviation for the sample means decreases with increasing sample sizes.

### What happens to the mean and standard deviation when the sample size decreases?

The population mean for the distribution of sample mean is the same as that of the distribution being scouted from. As a result, the standard deviation decreases as the sample size grows. However, as the sample sizes decrease, so does the standard deviation for the sample means.

### What happens to the mean as the sample size increases?

Increasing Sample Size With an infinite number of random samples, the mean distribution of the sampling is equal to the population average (u). Each sampling distribution becomes more leptokurtic as the sample size increases.

**Why is the sample size important? **

What is a sample size? Why is it important? The size of a sample refers to how many participants or observations are included in a study. Two statistical properties are affected by the size of a sample: 1) the precision and 2) the ability of the study’s conclusions.

#### Does the mean change with sample size?

The central limit theorem states, that the sampling distribution for the mean approaches a normal distribution as the sample size grows. As a result, the sample mean will approach the normal distribution as the sample size increases.

#### What happens as the sample size increases quizlet?

– As the sample size grows, the sample mean becomes closer to the population average. This means that the difference between the sample and population mean tends towards becoming smaller, i.e. close to zero.