properties of standard deviation
TRANSCRIPT
Properties of Standard DeviationBy: RIZWAN [email protected]
Properties of Standard Deviation
Standard deviation is only used to measure spread or dispersion around the mean of a data set.
Standard deviation is never negative. Standard deviation is sensitive to outliers. A single
outlier can raise the standard deviation and in turn, distort the picture of spread.
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 points are spread out over a large range of values.
The standard deviation of a statistical population, data set, or probability distribution is the square root of its variance.
The standard deviation of the sum of two random variables can be related to their individual standard deviations and the covariance between them:
where var stand for variance and cov covariance, respectively.
Properties of Standard Deviation
The sample standard deviation can be computed as:
It shows how much variation or "dispersion" exists from the average (mean, or expected value).
For data with approximately the same mean, the greater the spread, the greater the standard deviation.
If all values of a data set are the same, the standard deviation is zero (because each value is equal to the mean).
Properties of Standard Deviation
When analyzing normally distributed data, standard deviation can be used in conjunction with the mean in order to calculate data intervals.
If = mean, S = standard deviation and x = a value in the data set, then about 68% of the data lie in the interval: - S < x < + S. about 95% of the data lie in the interval: - 2S < x < + 2S. about 99% of the data lie in the interval: - 3S < x < + 3S.
Combined Standard Deviation(( N
1 × ( s
12 + d
12 ) + N
2 × ( s
22 + d
22 ) )/( N1 + N2 ))
Properties of Standard Deviation
GOOD BYE THANKS