Magazine

# Standard Deviation and Variance

last updated Friday, February 21, 2020
# #

  John Burson Subscribe

CONTENTS
A commonly used measure of dispersion is the standard deviation, which is simply the square root of the variance. The variance of a data set is calculated by taking the arithmetic mean of the squared differences between each value and the mean value. Squaring the difference has at least three advantages:
1. Squaring makes each term positive so that values above the mean do not cancel values below the mean.

2. Squaring adds more weighting to the larger differences, and in many cases, this extra weighting is appropriate since points further from the mean may be more significant.

3. The mathematics are relatively manageable when using this measure in subsequent statistical calculations.

Because the differences are squared, the units of variance are not the same as the units of the data. Therefore, the standard deviation is reported as the square root of the variance and the units then correspond to those of the data set.

The calculation and notation of the variance and standard deviation depend on whether we are considering the entire population or a sample set. Following the general convention of using Greek characters to express population parameters and Arabic characters to express sample statistics, the notation for standard deviation and variance is as follows:

σ  =  population standard deviation

σ 2  =  population variance

s  =  estimate of population standard deviation based on sampled data

s2  =  estimate of population variance based on sampled data

The population variance is defined as:

N
 (xi - μ)2 ______ N
σ2  =   Σ
i=1

The population standard deviation is the square root of this value.

The variance of a sampled subset of observations is calculated in a similar manner, using the appropriate notation for sample mean and number of observations. However, while the sample means is an unbiased estimator of the population mean, the same is not true for the sample variance if it is calculated in the same manner as the population variance. If one took all possible samples of n members and calculated the sample variance of each combination using n in the denominator and averaged the results, the value would not be equal to the true value of the population variance; that is, it would be biased. This bias can be corrected by using ( n - 1 ) in the denominator instead of just n, in which case the sample variance becomes an unbiased estimator of the population variance.

This corrected sample variance is defined as:

n
 (xi - x-)2 ________________ n-1
s2    =     Σ
i=1

The sample standard deviation is the square root of this value.

Standard deviation and variance are commonly used measures of dispersion. Additional measures include the range and average deviation.

### Subscribe to Paperfree Magazine

EB5 Visa Consultants by Paperfree EB5 Program

Get dedicated service, from finding the right information to complex investment challenges.

Real estate investment strategies

### Multifamily investment strategy to boost investment portfolio returns.

Diversify in multifamily investment strategy to lower volatility and boost portfolio returns.

### Value add real estate strategy helps investors drive capital growth.

The value add real estate strategy's first goal is capital growth, the second goal is some income. The strategy works with all property types

### Investing in senior housing to drive stable returns.

Senior living investments will create social impact on the market with strong fundamentals: growing demand, resilience to economic cycles.

### Invest in build to rent investment funds

Build to rent investment funds for passive real estate investing.

### Invest In Real Estate Private Equity

Discover diverse private equity real estate investment opportunities.

### Core real estate investment strategy to drive income vs capital growth

Core Real Estate Strategy is one of the most conservative modern real estate investment strategies focusing primarily on income.

### Passive real estate investing, best investment strategies, opportunities and more.

Passive real estate investing allow you to be a silent partner in large-scale real estate investments that can produce earnings and return on investment.

### Invest in Syndication Real Estate

Investing in real estate syndicates as a part of alternative investments strategy

### Investing in apartment buildings

Apartment investments are a sound investment option for numerous investment strategies.

### Multifamily fund

Multifamily funds have one of the highest average annual returns of all real estate investments. Find private and public multifamily investment funds below.

### Multifamily value add strategy

The main attribute of the multifamily value add strategy is the focus on capital growth. The investment strategy has a median risk profile.

### Core plus investment strategy real estate to generate income

Core Plus Strategy focus to generate income based on mid-low risk profile. Learn more.

### Opportunistic real estate investment to maximize return on investment

Opportunistic real estate investment strategy drives capital growth with heights risk of default.

### EB 5 investment projects list

Find the best fit for your immigration strategy and investment goals for EB5 projects in USA local markets.

### Value add real estate funds

Value add real estate funds aim to increase cash flow and value by buying and improving underutilized assets, potentially yielding higher returns than traditional real estate investments.