The definition of standard deviation is an arithmetical term that provides a good suggestion of volatility. It shows how usually values are dispersed from the average. Dispersion is the variation between the real value and the average value. The bigger variation between the final values, the standard value and the upper standard deviation will be the upper volatility. Earlier, the final prices are to the standard price, the lower the standard deviation and the lower volatility.
Standard Deviation Definition:
The definition of standard deviation is a statistical compute of spread or variability. The standard deviation is a
root mean square deviation of the principles from their arithmetic mean.
Variance Definition:
The square of the standard deviation. A measure of the degree of extends among a set of values a compute of the tendency of individual values to differ from the mean value.
The standard deviation is then, the same to the square root of that number.
Ex 1: The heights are: 500m, 370m, 70m, 330m and 200m. Find out the Mean, the Variance, and the Standard Deviation.
Sol: Step 1: Mean:
Mean = (500 + 370 + 70 + 330 + 200) / 5
= 1470 / 5
Mean = 294
So the average height is 294 mm.
To estimate the Variance, get each difference, square it, and then average the result:
Step 2: Variance:
σ^{2} = (206^{2} + 76^{2} + (- 224)^{2} + 36^{2} + (- 94)^{2}) / 5
= 108520 / 5
Variance = 21704.
So, the Variance is 21,704.
And the Standard Deviation is the square root of Variance, so:
Step 3: Standard Deviation:
σ = √21,704
σ = 147
And the excellent object regarding the Standard Deviation is so as to it is helpful.
So, Standard Deviation = 147.
Ex 2: Compute the standard deviation for the subsequent model facts 2, 4, 8, 6, 10, and 12. Establish the Mean, the Variance, and the Standard Deviation.
Sol: Step 1: Mean:
Mean = (2 + 4 + 8 + 6 + 10 + 12) / 6
= 42 / 6
= 7
To estimate the Variance, get each difference, square it, and then average the result:
Step 2: Variance: σ^{2} = ((5) ^{2}+ (3) ^{2}+ (-1) ^{2}+ (1) ^{2}+ (-3) ^{2}+ (-5) ^{2})/6
σ^{2} = (25+9+1+1+9+25)/6
= 70/6
= 11.67
So, the Variance is 11.67,
And the Standard Deviation is now the square root of Variance, so:
Step 3: Standard Deviation:
σ = √11.67
= 3.42
Ex 3: Find the Standard deviation of 1, 2, 3, 4, and 5?
Sol: Step 1: Calculate the mean and deviation.
X = 1, 2, 3, 4, 5
M = (1 + 2 + 3 + 4 + 5) / 5
= 3
Step 2: Variance: σ^{2} = ((1) ^{2}+ (2) ^{2}+ (3) ^{2}+ (4) ^{2}+ (5) ^{2})/5
σ^{2} = (1+4+9+16+25)/5
= 55/5
= 11
So, the Variance is 11,
And the Standard Deviation is now the square root of Variance, so:
Step 3: Standard Deviation:
σ = √11
= 3.32