The difference between the highest and lowest values in a data set.

Variance

The variability of scores

Calculated by the sums of deviations from the mean(squared) divided by n-1.

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STD DEV and SEM

Standard deviation represents the difference from the mean, how much scores differ from the mean.

Standard Error of the Mean (SEM) is how well the sample mean estimates to the population mean. Therefore variation in the sample = the 'error' in estimating the population mean.

The equation for SEM is STDDEv of the sample/square root of N.

A larger sample will yield a smaller SEM value.

SEM is used to calculate confidence intervals and error bars in graphs.

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The Normal Distribution

This is a family of distribution, with the area under the curve representing 100% of the sample.

The bell curve (aka the normal curve) can be seen with continuous variables, with scores closer to the mean appearing more frequent.

The most extreme values are found at the tails of the curve, the tails approach x but never actually touch.

The mean, mode and median are all very similar.

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Sample types

Smaller samples

Lead to HIGH sampling errors

Relatively varied sample means

Larger samples

Lead to LOW sampling errors

Have generally stable sampling means

The sample distribution of the mean is a normal distribution.

Larger samples mean that there are smaller confidence intervals. This is because there need to be more specific estimates.

A confidence interval is an interval estimate of the population parameters. 95% of the area under a normal curve is in the interval 1.96 SD away from the mean.

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