For 2 4 5 6 8: σ=2.2361
For 2 3 4: σ=1
3.4163.4163.4163.416
For 2 6 1 4 2 2 4 3 2: σ=1.5366
Consider thatxd= x- Arithmetic meand211-1.5 = -0.50.2522-1.5 = 0.50.25=0.5Arithmetic mean = (1+2)/2 =1.5Standard deviation=ie .5= 0.70now Considerxd= x- Arithmetic meand211-2=-1122-2=0033-2=11Arithmetic mean= (1+2+3)/3 = 2 =2Standard deviation= = (2/2) = 1So the Standard deviation can increasenow Considerxd= x- Arithmetic meand211-1.25=-0.250.062522-1.25=0.750.562511-1.25=-0.250.062511-1.25=-0.250.0625Arithmetic mean= (1+2+1+1)/4= 1.25 = .75Standard deviation= = (0.75/4) = 0.4330So the Standard deviation can decreaseStandard deviation can either decrese or increase or remains the same
Variability is determined by the how numbers are distributed across the set of numbers. There are several ways of measuring this the most common is standard deviation. To find standard deviation you first find the average of the set by adding them all up and dividing by the amount of numbers in the set. Then you find the square of each number in the set minus the average. You add all these values up, multiply them by 1/the number of items in the set, and take the square root. As an example the set {2,5,3,6} has much less variability as measured by the standard deviation than {2000,-1000,-500,484} even though they both have the same average. The firsts average is (2+5+3+6)/4 or 4. The standard deviation is the square root of(((2-4)^2+(5-4)^2+(3-4)^2+(6-4)^2)*1/4) or about 1.58113883. The standard deviation of the second set that has the same average as the first is the square root of (((2000-4)^2+(-1000-4)^2+(-500-4)^2+(484-4)^2)*1/4) or 1170.09059.
Standard deviation is the square root of the variance. Since you stated the variance is 4, the standard deviation is 2.
Standard deviation is the square root of the mean. The mean for this set is (2 + 4 + 3 + 7)/4 = 16/4 = 4; the square root of this is 2.
For 2 3 4: σ=1
Variance = 17.9047619 Standard Deviation = 4.23140188
3.4163.4163.4163.416
7.087547766 is the standard deviation for those figures.
1. establishment of standard 2. fixation of the standard 3. compairing actual performance with standard performance 4. finding out the deviation 5. correcting the deviation
5.142857143 is the mean.12.43956044 is the variance.3.526976104 is the standard deviation.
The SD is 2.
For 2 6 1 4 2 2 4 3 2: σ=1.5366
Consider thatxd= x- Arithmetic meand211-1.5 = -0.50.2522-1.5 = 0.50.25=0.5Arithmetic mean = (1+2)/2 =1.5Standard deviation=ie .5= 0.70now Considerxd= x- Arithmetic meand211-2=-1122-2=0033-2=11Arithmetic mean= (1+2+3)/3 = 2 =2Standard deviation= = (2/2) = 1So the Standard deviation can increasenow Considerxd= x- Arithmetic meand211-1.25=-0.250.062522-1.25=0.750.562511-1.25=-0.250.062511-1.25=-0.250.0625Arithmetic mean= (1+2+1+1)/4= 1.25 = .75Standard deviation= = (0.75/4) = 0.4330So the Standard deviation can decreaseStandard deviation can either decrese or increase or remains the same
If all four numbers are the same, there is no standard deviation. The mean will be equal to all 4 numbers, resulting in a 0 standard deviation. Ex) 5,5,5,5