The sample variance is obtained by dividing SS by the degrees of freedom (n-1). In this case, the sample variance is
SS/(n-1) = 300/(4-1) = 300/3 = 100
In order to get the standard error, you can do one of two things:
a) divide the variance by n and get the square root of the result:
square.root (100/4) = square.root(25) = 5, or
b) get the standard deviation and divide it by the square root of n.
10/square.root(4) = 10/2 = 5
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
5
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
z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
0.666666666667
The sample variance (s²) is calculated using the formula ( s² = \frac{SS}{n - 1} ), where SS is the sum of squares and n is the sample size. For a sample size of n = 9 and SS = 72, the sample variance is ( s² = \frac{72}{9 - 1} = \frac{72}{8} = 9 ). The estimated standard error (SE) is the square root of the sample variance divided by the sample size, calculated as ( SE = \sqrt{\frac{s²}{n}} = \sqrt{\frac{9}{9}} = 1 ). Thus, the sample variance is 9 and the estimated standard error is 1.
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
5
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
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.
z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
1,7,1
The variance is: 6.0
The variance is: 0.666666666667
T score is usually used when the sample size is below 30 and/or when the population standard deviation is unknown.
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.