Standard Deviation Shows

 Standard Deviation Shows

 

Education Introduction to standard deviation shows: In statistics, the standard deviation shows about the statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though practically less robust than average absolute deviation. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data spread over a large range of values. Standard Deviation Shows: Standard deviation shows that the variation for the given set of data’s. This Standard deviation shows the variation from population, a data set, and probability distribution etc… Formulas to which shows the standard deviation are, Mean: `barx` = `( sum(x) ) / n` Standard deviation: S =` sqrt(((sum(x - barx)^2)) / (n-1))` By using these formulas we can able to shows the variations for the set of data's. Understand equation solver is always challenging for me but thanks to all math websites to help me out. Example

 for the Standard Deviation Shows: Example for standard deviation shows 1: Here are 4 measurements 56, 57.,51 and 55. Calculate standard deviation for the given measurements Solution: Average, Mean ` barx` = `(56 + 57 + 52 + 55) / 4` = `220 / 4` = 55 Standard Deviation, S = ` sqrt(( ( 56 - 55 )^2 + ( 57 - 55 )^2 + ( 51 - 55 )^2 + ( 55 - 55 )^2) / (4 - 1))` = `sqrt((( 1 )^2 + ( 2 )^2 +( -3 )^2 + ( -0 )^2 )/ 3) ` = `sqrt(14 / 3) ` S = `sqrt(4.66667)` Standard Deviation `S = 2.1602` Answer: Thus the Standard Deviation ` S = 2.1602` is shows the deviation from the given data's. Example for standard deviation shows 2: there were a data set with 4 values as 76, 70, 71 and 75. Calculate shows the standard deviation Solution: Average, Mean ` barx` = `(77 + 71 + 73 + 75) / 4` = `296 / 4` = 74 Standard Deviation, S = ` sqrt(( ( 77 - 74)^2 + (71 - 74 )^2 + ( 73 - 74 )^2 + ( 75 - 74 )^2) / (4 - 1))` = `sqrt((( 3 )^2 + ( -3 )^2 +( -1 )^2 + ( 1 )^2 )/ 3) ` = `sqrt(20 / 3) ` S = `sqrt(6.66667)` Standard Deviation `S = 2.581` Answer: Thus the Standard Deviation ` S = 2.581``is shows the deviation from the given data's.`

 Example for standard deviation shows 3: Calculate the mean and standard deviation for the given dataset. i X 1 2400 2 3800 3 4900 4 5700 5 6500 6 7400 Solution: `barx` = `( 2400 + 3800 + 4900 + 5700 + 6500 + 7400) / 6` = 5116 `x` `x - barx` ` ( x - barx)^2` 2400 2400 - 5116 = -2716 7376656 3800 3800 - 5116 = -1316 1731856 4900 4900 - 5116 = -216 46656 3700 5700 - 5116 = -584 341056 6500 6500 - 5116 = 1384 1915456 7400 7400 - 5116 = 2284 5216656 ` (x - barx)^2` =16628336 S = `sqrt( 16628336 / 5 )` S = `sqrt( 3325667.2 )` ` S = 1823.64119` Answer: `barx` ` = 4116` `S = 1823.64119` Thus, the Standard Deviation shows that the data set has found. Learn more on about derivative of cos^2x and its Examples. Between, if you have problem on these topics history of calculus, Please share your comments.