Variance
mean
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
The mean of a distribution of scores is the average.
It is 68.3%
Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.
Variance
mean
Standard deviation
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
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.
The mean of a distribution of scores is the average.
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)].
It is 68.3%
Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.
If the standard deviation of 10 scores is zero, then all scores are the same.
IQ scores are standardized by age, with a mean of 100 and a standard deviation of 15. So, the average IQ for a 27-year-old woman would also be around 100, with a range of scores considered within the normal distribution.
Yes. It will increase the standard deviation. You are increasing the number of events that are further away from the mean, and the standard deviation is a measure of how far away the events are from the mean.