mean
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
Variance
If the standard deviation of 10 scores is zero, then all scores are the same.
Since the standard deviation is zero, the scores are all the same. And, since their mean is 10, they must all be 10.
Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller. Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller. Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller. Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller.
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
Variance
Variance
If the standard deviation of 10 scores is zero, then all scores are the same.
Standard deviation
Standard Deviation tells you how spread out the set of scores are with respects to the mean. It measures the variability of the data. A small standard deviation implies that the data is close to the mean/average (+ or - a small range); the larger the standard deviation the more dispersed the data is from the mean.
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.
All the scores are equal
Since the standard deviation is zero, the scores are all the same. And, since their mean is 10, they must all be 10.
Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller. Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller. Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller. Because the standard deviation is a measure of the spread in scores. As individuals score more similarly, the spread gets smaller.
The answer depends on the degrees of freedom (df). If the df > 1 then the mean is 0, and the standard deviation, for df > 2, is sqrt[df/(df - 2)].
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