Weighted Standard Deviation

By Author: Pierce Brosnan
Total Articles: 127
Comment this article

Introduction:

A statistic used as a measeure of the dispersion in the distribution or variation equal to the square root of the arithmetic mean of the square of the deviation from the arithmetic mean.

Modern portfolio theory:

The theory was invited by tries to maximize return and minimize risk carefully choosing the different assets. Although it is widely used in the financial industry and several creator of Nobel prize for the theory , in recent years the basic assumption of MPT have widely challenged by fields such economics

MPT is formulation of the concept of diversification in investing, the aim of selecting a collection of assists has collectively lower risk than any individual asset. This possible different type of assets often change value in opposite ways. Example the prices in the stock market fall, the prices in the bond market often increase, the vice versa. A collection of both bye asset can lower over all risk either individually.

More technically it model an assets return as normally distributed random variable risk as the standard deviation or return, and models a portfolio ...
... as weighted combination of assets so that the return of portfolio is the weighted combination of assets return. By returns are not correlated. MPT seeks to reduce the total variance of the portfolio.

Standard Deviation:

The statistical population a data, set, probability distribution is the square root of variance. Standard variance is widely used measure the variability dispersion. The algebra more tractable thought practice less robust that the expected deviation or average absolute deviation.

The Example. The average height of adult men in the US is about 70 inches as 178 cm the deviation is 3 inches as 8 cm . The means that most men about 68 percent normal in distribution. Have height within 8cm.

So the standard deviation is 67-73 in 170-185cm is one of the standard derivation.

In addition to express the variability of a population standard deviation is used to measure confidence statistical conclusion for example the expected standard deviation in the result if the same poll were to be conducted the multiplied times. The report margin or error in typically about the twice the standard deviation.

The term standard deviation is by Karl pea son in 1894 used it in lecture. This was replacement for earlier alternative names for the name idea. A property of standard deviation is that unlike variance. It is expressed in the same unit as the data however that is easement with percentage.

Problem in Standard Deviation

Standard Deviation:

The value to mention the standard deviation.

2+3+4+5+6/4= 20/4 =5.

Estimation:

One find the standard deviation of an entire population in cases where every number of a population is sampled. The standard deviation duo is estimated by examine a random sample taken from the population.

Simple standard deviation:

The most common estimation for used `sigma` adjustment version the sample standard derivation denoted by s be defined by

Other estimator:

Further Information: Unbiased estimation

The unbiased estimator is know when random variable is normally distributed the formula complicated and amount to a minor correction.

Comprehend more on about What is a Mode in Math and its Circumstances. Between, if you have problem on these topics Define Histogram Please share your views here by commenting.