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When computing the sample variance the sum of squared deviations about the mean is used for what reason?
You want some measure of how the observations are spread about the mean. If you used the deviations their sum would be zero which would provide no useful information. You could use absolute deviations instead. The sum of squared deviations turns out to have some useful statistical properties including a relatively simple way of calculating it. For example, the Gaussian (or Normal) distribution is completely defined by its mean and variance.
Why do you square the deviations to get the variance and then take the reverse action of taking the square root of the variance to return the variance to sigma?
because of two things- a) both positive and negative deviations mean something about the general variability of the data to the analyst, if you added them they'd cancel out, but squaring them results in positive numbers that add up. b) a few larger deviations are much more significant than the many little ones, and squaring them gives them more weight. Sigma, the square root of the variance, is a good pointer to how far away from the mean you are likely to be if you choose a datum at random. the probability of being such a number of sigmas away is easily looked up.
Is the variance of a group of scores the same as the sum of the squared deviations or the average of the squared deviations?
Given a set of n scores, the variance is sum of the squared deviation divided by n or n-1. We divide by n for the population and n-1 for the sample.
Why are variances squared?
The variances are squared so that all deviations above and below the mean become positive values. Taking the square root of the variance then gives a measure of the differences from the mean: the standard deviaton. Squaring the deviations also makes the bigger differences stand out. Look at 100 squared vs 10 squared.
How many standard deviations is 16.50 from the mean?
How many standard deviations is 16.50 from the mean?
