A Few CLT-Related Terms

– Mean
The mean is the most common indicator of an ‘average’ score. It is computed by dividing the sum of all scores by the number of scores. If the distribution has extreme outliers and/or skew, the mean may not be very descriptive of a ‘typical’ score. More | Formula


– Standard deviation
The standard deviation is a common measure of variation of scores. The standard deviation is computed by taking the square root of the variance. The larger the standard deviation (and variance), the wider the distribution and the further the scores are from the mean. Like the mean, the standard deviation is sensitive to outlying scores. Formulas


– Variance
Variance is a measure of how much scores in a distribution vary from the mean. Mathematically, variance is the average of the squared deviations from the mean. Taking the square root of variance results in the standard deviation. Formulas


– Population versus sample
A population consists of all cases in the group of interest. A sample is a group of cases selected from all possible cases in the population. For example, if the group of interest is American working women, the population would include each and every working woman in America. Usually it is impossible to collect data on an entire population. Instead, we use one of many sampling techniques to select a subgroup from the population. This subgroup is a sample.


– Sample size
A sample is a subset taken from the population of interest. The number of sampled cases is called the sample size.


– Sampling distribution of the mean
The sampling distribution of the mean is a theoretical distribution. If you were to draw an infinite number of samples with a particular sample size from a population you would get an infinite number of sample means (one for each sample you drew). The distribution of these means is the sampling distribution of means for your population at that particular sample size. More


– Normal distribution
The normal curve (also called the “Bell curve” or “the Gaussian distribution”) is a theoretical distribution mathematically defined by its mean and variance. When graphed the normal distribution has a shape similar to a bell curve (see Figure below). Naturally occurring distributions are rarely normal in shape. However, the distributions of many chance events do approach normal shape. Importantly, the distribution of possible means for a randomly selected sample is approximately normal if the sample is sufficiently large. The area under the curve for a standardized normal curve is exactly 1.00 or 100%, which is useful for finding probabilities.


Figure. Three normal distributions whose means and standard deviations vary.