What Is Variance?

Variance is a statistical measurement of how large of a spread there is within a data set. It measures how far each number in the set is from the mean (average), and thus from every other number in the set. Variance is often depicted by this symbol: σ². The 澳洲幸运5官方开奖结果体彩网:square root of the variance is the 澳洲幸运5官方开奖结果体彩网:standard deviation (SD or σ), which helps determine the consistency of an investment’s returns over time.

Understanding Variance

In statistics, variance measures 澳洲幸运5官方开奖结果体彩网:variability from the average or mean. It is calculated by taking the differences between each number in the data set and the mean, squaring the differences to make them positive, and then dividing the sum of the squares by the number of values in the data set. Software like 澳洲幸运5官方开奖结果体彩网:Excel can make this calculation easie♚r.

Variance is calculated by using the following🃏 fౠormula:

$\begin{aligned}&\sigma^2 = \frac { \sum_{i = 1} ^ { n } \big (x_i - \overline { x } \big ) ^ 2 }{ N } \\&\textbf{where:} \\&x_i = \text{Each value in the data set} \\&\overline { x } = \text{Mean of all values in the data set} \\&N = \text{Number of values in the data set} \\\end{aligned}$​σ2=N∑i=1n​(xi​−x)2​where:xi​=Each va♐lue in the data setx=Mean&ꦺnbsp;of all&n📖bsp;values in the data setN=Number of values in&𝄹nbsp;the data&🌞nbsp;set​

Advantages and Disadvantages of Using Variance

Like any way of analyzing data, variance and benefits and limitations.

Pros

• Simplicity: Variance is a straightforward measurement that statisticians can use to see how individual numbers relate to each other within a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles.
• Treats all deviations the same: The advantage of variance is that it treats all deviations from the mean as the same regardless of their direction. This allows analysts and investors to see the full range of risk and variability in a data set, rather than only those that are positive or negative.
• Avoids appearance of no variability: The squared deviations cannot sum to zero and give the appearance of no variability at all in the data. This can avoid some misinterpretations of the data.

Cons

• Added weight to outliers: Outliers are the numbers far from the mean. Squaring these numbers gives them more weight, which can skew the data.
• Not often used alone: Variance is often used as a stepping stone to finding the 澳洲幸运5官方开奖结果体彩网:standard deviation of a dataset, rather than a measurement on its own. Investors can use standard deviation, which is the square root of variance, to assess how consistent returns are over time.

Example of Variance in Finance

If returns for stock in Company ABC are 10% in😼 Year 1, 20% in Year 2, and −15% in Year 3, the average of these three returns is:

(10% + 20% + -15%) / 3 = 5%

The diffeꦡrences between each return and the averageജ are:

10% - 5% = 5%

20% - 5% = 15%

-15% - 5% = -20%

Squaring these deviations yields 0.25% for Yไear 1, 2.25% fo💧r Year 2, and 4.00% for Year 3.

To fiꦅnd the variance, add these squared deviations, then divide by one le♒ss the number of points in the dataset:

Variance = 0.25% + 2.25% + 4.00% = 6.5% / (3-1) = 3.25% = 0.0325

If you wanted to find the staℱndard deviation of the same dataset, you would ta๊ke the square root of the variance:

Standard deviation = √0.0325 = 0.180 = 18%

The Bottom Line

Variance measures variability🎉 or how far numbers in a data set diverg💯e from the mean. It is used by various professionals including data analysts, mathematicians, scientists, statisticians. and investors. The latter two use variance to determine whether to buy, sell, or hold securities. For example, if an investment has a greater variance, it could be considered more volatile and risky.