The further the data points from the mean, the higher this measure of spread.
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Standard deviation and variance are two basic mathematical concepts that have an important place in various parts of the financial sector, from accounting to economics to investing. Both measure the variability of figures within a data set using the mean of a certain group of numbers. They are important to help determine volatility and the distribution of returns. But there are inherent differences between the two. While standard deviation measures the square root of the variance, the variance is the average of each point from the mean. Show
Key Takeaways
1:14 What Is Variance?Standard DeviationStandard deviation is a statistical measurement that looks at how far a group of numbers is from the mean. Put simply, standard deviation measures how far apart numbers are in a data set. This metric is calculated as the square root of the variance. This means you have to figure out the variation between each data point relative to the mean. Therefore, the calculation of variance uses squares because it weighs outliers more heavily than data that appears closer to the mean. This calculation also prevents differences above the mean from canceling out those below, which would result in a variance of zero. But how do you interpret standard deviation once you figure it out? If the points are further from the mean, there is a higher deviation within the data. But if they are closer to the mean, there is a lower deviation. So the more spread out the group of numbers are, the higher the standard deviation. As an investor, make sure you have a firm grasp on how to calculate and interpret standard deviation and variance so you can create an effective trading strategy. VarianceA variance is the average of the squared differences from the mean. To figure out the variance, calculate the difference between each point within the data set and the mean. Once you figure that out, square and average the results. For example, if a group of numbers ranges from one to 10, you get a mean of 5.5. If you square the differences between each number and the mean and find their sum, the result is 82.5. To figure out the variance:
Note that the standard deviation is the square root of the variance so the standard deviation is about 3.03. The mean is the average of a group of numbers, and the variance measures the average degree to which each number is different from the mean. The extent of the variance correlates to the size of the overall range of numbers, which means the variance is greater when there is a wider range of numbers in the group, and the variance is less when there is a narrower range of numbers. Key DifferencesOther than how they're calculated, there are a few other key differences between standard deviation and variance. Here are some of the most basic ones.
The table below summarizes some of the key differences between standard deviation and variance. Key Differences Between Standard Deviation and Variance Standard DeviationVarianceWhat Is it? The square root of the varianceThe average squared differences from the mean What Does it Indicate?The spread between numbers in a data setThe average degree to which each point differs from the mean How Is it Expressed?The same as the units in the data setIn squared units or as a percentageWhat Does it Mean?A low standard deviation (spread) means low volatility while a high standard deviation (spread) means higher volatilityThe degree to which returns vary or change over time Standard Deviation and Variance in InvestingThese two concepts are of paramount importance for both traders and investors. That's because they are used to measure security and market volatility, which plays a large role in creating a profitable trading strategy. Standard deviation is one of the key methods that analysts, portfolio managers, and advisors use to determine risk. When the group of numbers is closer to the mean, the investment is less risky. But when the group of numbers is further from the mean, the investment is of greater risk to a potential purchaser. Securities that are close to their means are seen as less risky, as they are more likely to continue behaving as such. Securities with large trading ranges that tend to spike or change direction are riskier. Risk in and of itself isn't necessarily a bad thing in investing. That's because riskier investments tend to come with greater rewards and a larger potential for payout. Example of Standard Deviation vs. VarianceTo demonstrate how both principles work, let's look at an example of standard deviation and variance. Suppose you have a series of numbers and you want to figure out the standard deviation for the group. The numbers are 4, 34, 11, 12, 2, and 26. We need to determine the mean or the average of the numbers. In this case, we determine the mean by adding the numbers up and dividing it by the total count in the group: (4 + 34 + 18 + 12 + 2 + 26) ÷ 6 = 16 So the mean is 16. Now subtract the mean from each number then square the result:
Now we have to figure out the average or mean of these squared values to get the variance. This is done by adding up the squared results from above, then dividing it by the total count in the group: (144 + 324 + 4 + 16 + 196 + 100) ÷ 6 = 130.67 This means we end up with a variance of 130.67. To figure out the standard deviation, we have to take the square root of the variance, which is 11.43 What Does Variance Mean?The simple definition of the term variance is the spread between numbers in a data set. Variance is a statistical measurement used to determine how far each number is from the mean and from every other number in the set. You can calculate the variance by taking the difference between each point and the mean. Then square and average the results. What Does Standard Deviation Mean?Standard deviation measures how data is dispersed relative to its mean and is calculated as the square root of its variance. The further the data points are, the higher the deviation. Closer data points mean a lower deviation. In finance, standard deviation calculates risk so riskier assets have a higher deviation while safer bets come with a lower standard deviation. What Is Variance Used for in Finance and Investing?Investors use variance to assess the risk or volatility associated with assets by comparing their performance within a portfolio to the mean. For instance, you can use the variance in your portfolio to measure the returns of your stocks. This is done by calculating the standard deviation of individual assets within your portfolio as well as the correlation of the securities you hold. What Are the Shortcomings of Variance?The variance of an asset may not be a reliable metric. Calculating variance can be fairly lengthy and time-consuming, especially when there are many data points involved. Variance doesn't account for surprise events that can eat away at returns. And variance is often hard to use in a practical sense not only is it a squared value, so are the individual data points involved. What is a measure of spread from the mean?The variance and the standard deviation are measures of the spread of the data around the mean. They summarise how close each observed data value is to the mean value. In datasets with a small spread all values are very close to the mean, resulting in a small variance and standard deviation.
Is the measure of how far the data is spread from the mean?The standard deviation is a number that measures how far the data are spread from the mean. Let a calculator or computer do the arithmetic. The standard deviation, s or σ, is either zero or larger than zero.
What measures the spread of dispersion from the mean?Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations.
What is the meaning of and is it a measure of spread or a measure of center?Center describes a typical value of a data point. Two measures of center are mean and median. Spread describes the variation of the data. Two measures of spread are range and standard deviation.
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