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%
Yes, a normal distribution can have a standard deviation of 1. In fact, the standard normal distribution, which is a specific case of the normal distribution, has a mean of 0 and a standard deviation of 1. This allows for easy computation of z-scores, which standardize any normal distribution for comparison. Therefore, a normal distribution with a standard deviation of 1 is a valid and common scenario.
Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.
If the mean score is 100 and the standard deviation is 15, the distribution of scores is likely to follow a normal distribution, also known as a bell curve. In this distribution, approximately 68% of scores fall within one standard deviation of the mean (between 85 and 115), about 95% fall within two standard deviations (between 70 and 130), and about 99.7% fall within three standard deviations (between 55 and 145). This pattern indicates that most scores cluster around the mean, with fewer scores appearing as you move away from the center.
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.