Sum(X) = 37
Sum(X2) = 289
Var(X) = Sum(X2) - sum(X)2/n = 289 - 37*37/5 = 15.20
- 4
The range = the difference between the highest and the lowest values in the data set. For example if I had a data set like this: 10, 20, 30, 40, 50 50 is the highest number and 10 is the lowest number. 50-10= 40. 40= the range of the above data set.
n = sample sizen1 = sample 1 sizen2 = sample 2 size= sample meanμ0 = hypothesized population meanμ1 = population 1 meanμ2 = population 2 meanσ = population standard deviationσ2 = population variance
mean = 5, variance = 5
Standard Deviation = (principal value of) the square root of Variance. So SD = 10.
The variance is: 3.8
The variance is 13.5833
- 4
For 12 10 9 7 7: var=4.5
The variance is: 500.0
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 larger your sample size, the less variance there will be. For instance, your information is going to be much more substantial if you took 1000 samples over 10 samples.
6.3
The variance is 10.
First mean is calculated.Then calculate deviations from the mean.Then the deviations are squared.Then the squared deviations are summed up.Finally this sum is divided by number of items for which the variance is being calculated. For a population, it is by the number of values, in this case 12. If it is a sample, then we divide by one less, which is 11,For these figures, the variance for the population is 11069.24306. If it is a sample, it is 12075.53788 as the result.
The variance of the numbers 1 7 10 and 3 is: 16.25
mean =(5+9+10+2+7+9+14)/7=8 s^2 = Variance = (1/7){(5-8)^2+(9-8)^2+(10-8)^2+(2-6)^2+(7-8)^2+(9-8)^2+(14-8)^2}=14.6666 Standard deviation =s= sqrt(14.6666)=3.8297