The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
Variance
5
mean
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.
Variance
Variance
5
mean
The variance and the standard deviation will decrease.
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.
If the standard deviation of 10 scores is zero, then all scores are the same.
All the scores are equal
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.
A variable that has been transformed by multiplication of all scores by a constant and/or by the addition of a constant to all scores. Often these constants are selected so that the transformed scores have a mean of zero and a variance (and standard deviation) of 1.0.
Since the standard deviation is zero, the scores are all the same. And, since their mean is 10, they must all be 10.
sum of scores: 24 mean of scores : 24/4 = 6 squared deviations from the mean: 9, 4,4,9 sum of these: 26 sample variance: 26/4 = 6.5