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It depends what percentage of the total data you want to embrace. 99.73% of the total distribution lies between minus to plus 3 standard deviations. That's usually the benchmark range.
6
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.
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.
The cumulative probability up to the mean plus 1 standard deviation for a Normal distribution - not any distribution - is 84%. The reference is any table (or on-line version) of z-scores for the standard normal distribution.
T-scores have a mean of 50 and a standard deviation of 10. These values are fixed and do not change regardless of the distribution of T-scores.
Standard deviation
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.
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.
The cumulative probability up to the mean plus 1 standard deviation for a Normal distribution - not any distribution - is 84%. The reference is any table (or on-line version) of z-scores for the standard normal distribution.
z=(x-mean)/(standard deviation of population distribution/square root of sample size) T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute. t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)
All the scores are equal
The standard deviation (SD) is a measure of spread so small sd = small spread. So the above is true for any distribution, not just the Normal.
mean
Variance