What does the standard deviation tell you about the variability in a data set?

The range is the difference between the maximum and the minimum value of the data set. It allows you to know the gap between the data set.

Standard Deviation tells us how far a particular value is from the data set's mean. It tells us how far the data is spread from the mean.

We generally prefer standard Deviation over the range because it allows us to understand the data set's variability. In contrast, the range only tells us the difference between the maximum and the minimum value.

The standard deviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standard deviation.

But in situations where you just observe and record data, a large standard deviation isn’t necessarily a bad thing; it just reflects a large amount of variation in the group that is being studied.

For example, if you look at salaries for everyone in a certain company, including everyone from the student intern to the CEO, the standard deviation may be very large. On the other hand, if you narrow the group down by looking only at the student interns, the standard deviation is smaller, because the individuals within this group have salaries that are similar and less variable. The second data set isn’t better, it’s just less variable.

Similar to the mean, outliers affect the standard deviation (after all, the formula for standard deviation includes the mean). Here’s an example: the salaries of the L.A. Lakers in the 2009–2010 season range from the highest, $23,034,375 (Kobe Bryant) down to $959,111 (Didier Ilunga-Mbenga and Josh Powell). Lots of variation, to be sure!

The standard deviation of the salaries for this team turns out to be $6,567,405; it’s almost as large as the average. However, as you may guess, if you remove Kobe Bryant’s salary from the data set, the standard deviation decreases because the remaining salaries are more concentrated around the mean. The standard deviation becomes $4,671,508.

Here are some properties that can help you when interpreting a standard deviation:

• The standard deviation can never be a negative number, due to the way it’s calculated and the fact that it measures a distance (distances are never negative numbers).

• The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same (no deviation).

• The standard deviation is affected by outliers (extremely low or extremely high numbers in the data set). That’s because the standard deviation is based on the distance from the mean. And remember, the mean is also affected by outliers.

• The standard deviation has the same units of measure as the original data. If you're talking about inches, the standard deviation will be in inches.

  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.

  Key Takeaways

  • Standard deviation and variance are two key measures commonly used in the financial sector.
  • Standard deviation is the spread of a group of numbers from the mean.
  • The variance measures the average degree to which each point differs from the mean.
  • While standard deviation is the square root of the variance, variance is the average of all data points within a group.
  • The two concepts are useful and significant for traders, who use them to measure market volatility.

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  What Is Variance?

  Standard Deviation

  Standard 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.

  Variance

  A 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:

  • Divide the sum, 82.5, by N-1, which is the sample size (in this case 10) minus 1.
  • The result is a variance of 82.5/9 = 9.17.

  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 Differences

  Other 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.

  • Standard deviation measures how far apart numbers are in a data set. Variance, on the other hand, gives an actual value to how much the numbers in a data set vary from the mean.
  • Standard deviation is the square root of the variance and is expressed in the same units as the data set. Variance can be expressed in squared units or as a percentage (especially in the context of finance).
  • Standard deviation can be greater than the variance since the square root of a decimal is larger (and not smaller) than the original number when the variance is less than one (1.0 or 100%).
  • The standard deviation is smaller than the variance when the variance is more than one (e.g. 1.2 or 120%).

  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 Investing

  These 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. Variance

  To 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:

  • (4 - 16)2 = 144
  • (34 - 16)2 = 324
  • (18 - 16)2 = 4
  • (12 - 16)2 = 16
  • (2 - 16)2 = 196
  • (26 - 16)2 = 100

  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 does standard deviation Tell us about variability?

  The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.

  What does the standard deviation tell you about the variability in a data set quizlet?

  Standard deviation is a measure of variability which indicates an average relative distance between each data point and the mean. The larger the standard deviation, the more the data is spread out from the mean.

  What does the standard error tell you about the variability in a data set?

  Revised on November 17, 2022. The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.

  What is the relationship between variability and standard deviation?

  Unlike range and interquartile range, variance is a measure of dispersion that takes into account the spread of all data points in a data set. It's the measure of dispersion the most often used, along with the standard deviation, which is simply the square root of the variance.