The document discusses standard deviation and its properties. Standard deviation is a measure of how spread out numbers are from the average (mean) value. It is always non-negative and can be impacted by outliers. A low standard deviation means values are close to the mean, while a high standard deviation means values are more spread out. Standard deviation can be used to calculate what percentage of data falls within certain intervals from the mean when data is normally distributed.

1. By: RIZWAN SHARIF
rizichat@yahoo.com

2. 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.

3. 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.

4. 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).

5. 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
1
2 + d
1
2 ) + N
2
× ( s
2
2 + d
2
2 ) )/( N1 + N2 ))