Use Of Standard Deviation
Introduction
Introduction
The standard deviation calculates the variation of the data about the mean value. It is useful in equalizing the sets of data which may have the same mean but a variation in range.
A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
For example, each of the three populations {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has a mean of 7. Their standard deviations are 7, 5, and 1, respectively. The third population has a much smaller standard deviation than the other two because its values are all close to 7. It will have the same units as the data points themselves. If, for instance, the data set {0, 6, 8, 14} represents the ages of a population of four siblings in years, the standard deviation is 5 years. As another example, the population {1000, 1006, 1008, 1014} may represent the distances traveled by four athletes, measured in meters. It has a mean of 1007 meters, and a standard deviation of 5 meters.
Standard deviation may serve as a measure of uncertainty. In physical science, for example, the reported standard deviation of a group of repeated measurements gives the precision of those measurements. When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance: if the mean of the measurements is too far away from the prediction (with the distance measured in standard deviations), then the theory being tested probably needs to be revised. This makes sense since they fall outside the range of values that could reasonably be expected to occur if the prediction were correct and the standard deviation appropriately quantified.
Use of standard deviation deals with a set of data alike to zero point outs that all values in the set are the similar. use of Larger values imply that the independent data points are farther from the average value of standard deviation.
Use of Standard Deviation-definition
Standard Deviation is defined as the measure of describing the variability of the Data set. It is used for measuring the average of numbers in a set of data. Measurement of standard deviation is done by taking square root for the sum of mean difference with the given data divided by the total number of values subtracted by one.
It is nothing but standard deviation is calculated by taking square root for Variance.
For measuring standard deviation, mean has to be used. Mean formula is
'barx' = '(sum(x ))/(n)'
For measuring standard deviation the formula used is
S = 'sqrt((sum(x - barx))/(n - 1))'
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Use of Standard Deviation:
Standard deviation is a very good tool for evaluating the mixture of values in the given data.It gives the measurement by which the consistency and strength from the total mixture of values.
This measurement is about the type of error in standard deviation is called as Random Error.
In finance, standard deviation is used to determine the investment's precariousness.
Standard deviation is used by business investors as an estimate for the quantity of predictable unpredictability.
use of Standard deviation is given in step by step for calculating standard deviation:
Step I : Find the mean for the given n numbers in the Data set.
Step II : Find distance of each given numbers in the Data set from the mean. This is called "deviation" from the mean.
Step III : Take Square of each deviation value found From mean.
Step IV : Calculate the summation for the Squared standard deviations.
Step V : Now apply the Standard Deviation formula to calculate the Standard deviation form the mean.
Use of Standard Deviation-example Problem:
Calculate the standard deviation for the given data.
4,6,8,11,16
Solution:
Calculate the mean.
'barx' = '(sum(x))/(n)'
'barx' = '(4+6+8+11+16)/(5)'
'barx' = 9
Calculating standard deviation.
S = 'sqrt((sum(x - barx))/(n-1))'
S = 'sqrt(((4 - 9)^2+(6 - 9)^2+(8 - 9)^2+(11 - 9)^2+(16 - 9)^2)/(4))'
S = 4.69041576
by: nitinp
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