# Standard Deviation and Variance (2 of 2)

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although less sensitive to extreme scores than the

range,
the standard deviation is more sensitive than the

semi-interquartile
range. Thus, the standard deviation should be supplemented by the
semi-interquartile range when the possibility of extreme scores is
present.

If variable Y is a linear

transformation of
X such that:

Y = bX + A,

then the variance of Y is:

where

is
the variance of X.

The standard deviation of Y is bσ

_{x
} where σ

_{x} is the standard
deviation of X.

## Standard Deviation as a Measure of Risk

The standard deviation is often
used by investors to measure the risk of a stock or a stock portfolio.
The basic idea is that the standard deviation is a measure of volatility:
the more a stock's returns vary from the stock's average return, the
more volatile the stock. Consider the following two stock portfolios
and their respective returns (in per cent) over the last six months.
Both portfolios end up increasing in value from $1,000 to $1,058. However,
they clearly differ in volatility. Portfolio A's monthly returns range
from -1.5% to 3% whereas Portfolio B's range from -9% to 12%. The standard
deviation of the returns is a better measure of volatility than the
range because it takes all the values into account. The standard deviation
of the six returns for Portfolio A is 1.52; for Portfolio B it is 7.24.

How to compute
the standard deviation in SPSS.

**Further Reading:**
Risk
Management by Michel Crouhy et al.

The
Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns
and Minimize Risk by William J. Bernstein

Personal
Finance for Dummies by Eric Tyson

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