Psych 308 Quiz 2

Why can't we just average the deviations from the mean to index variability? What are two solutions? Which one is most commonly used and why?

Because it comes out zero. To fix it you can either take the absolute value of the scores or square the numbers. Normally the numbers are squared then unsquared because it is more statistically useful in the end.

What is standard deviation?

Standard deviation is a measure of variation around the mean. The mean is the point in the distribution where all of the deviations or distances people are from the mean above the mean equal those below the mean. So, if we just add up the deviations above and below, we get zero. Standard deviation is a way to capture amount of variability that gets around this problem by squaring the deviations, and then square-rooting them back. When you square the deviations you get rid of the negative sign. But, now you are in squared units not original units. So, we square root them back. Thus, standard deviation is the average deviation from the mean. In other words, it is the average degree to which scores in the distribution deviate from the mean - it is the average distance from the average.

How would you explain what the standard deviation formula does? You must talk about each symbol, each operation, and what it all does.

The top is the Sum of Squared deviations from the mean. For each person, you get the deviation of the mean from their score, and then you square that. Add up the squared deviations. Then, by dividing by N we get the average squared deviation. Lastly, when we square root it, we get the average deviation from the mean.

What is variance?

Variance is a measure of variation around the mean. The mean is the point in the distribution where all of the deviations or distances people are from the mean above the mean equal those below the mean. So, if we just add up the deviations above and below, we get zero. Variance is a way to capture amount of variability that gets around this problem by squaring the deviations. When you square the deviations you get rid of the negative sign. But, now you are in squared units not original units. So, variance is the average squared deviation from the mean.

What is the main reason why standard deviation is usually reported in studies rather than variance?

What is the main reason why standard deviation is usually reported in studies rather than variance?