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In this article, I decided to look at how standard deviation works in Excel using the STANDARDEVAL function. I just haven’t described or commented for a very long time, and also simply because it’s very useful feature for those who study higher mathematics. And helping students is sacred; I know from my own experience how difficult it is to master. In reality, standard deviation functions can be used to determine the stability of products sold, create prices, adjust or form an assortment, and so on, no less. useful analyzes your sales.

Excel uses several variations of this variance function:

Mathematical theory

First, a little about the theory, how you can describe the standard deviation function in mathematical language for using it in Excel, for analyzing, for example, sales statistics data, but more on that later. I warn you right away, I will write a lot unclear words...)))), if anything below in the text, look immediately practical application in the program.

What exactly does standard deviation do? It estimates the standard deviation of a random variable X relative to its mathematical expectation based on an unbiased estimate of its variance. Agree, it sounds confusing, but I think students will understand what we are actually talking about!

First, we need to determine the “standard deviation”, in order to subsequently calculate the “standard deviation”, the formula will help us with this: The formula can be described as follows: it will be measured in the same units as the measurements of a random variable and is used when calculating the standard arithmetic mean error, when constructing confidence intervals, when testing hypotheses for statistics, or when analyzing a linear relationship between independent variables. The function is defined as square root from the variance of the independent variables.

Now we can define and standard deviation is an analysis of the standard deviation of a random variable X relative to its mathematical perspective based on an unbiased estimate of its variance. The formula is written like this:
I note that all two estimates are biased. In general cases, it is not possible to construct an unbiased estimate. But an estimate based on an estimate of the unbiased variance will be consistent.

Practical implementation in Excel

Well, now let’s move away from the boring theory and see in practice how the STANDARDEVAL function works. I will not consider all variations of the standard deviation function in Excel; one is enough, but in examples. As an example, let’s look at how sales stability statistics are determined.

First, look at the spelling of the function, and as you can see, it is very simple:

STANDARD DEVIATION.Г(_number1_;_number2_; ….), where:

Now let's create an example file and, based on it, consider how this function works. Since to carry out analytical calculations it is necessary to use no less three meanings, as in principle in any statistical analysis, I also took conditionally 3 periods, this could be a year, a quarter, a month or a week. In my case - a month. For maximum reliability, I recommend taking as many periods as possible, but no less than three. All the data in the table is very simple for clarity of operation and functionality of the formula.

First, we need to calculate the average by month. We will use the AVERAGE function for this and get the formula: = AVERAGE(C4:E4).
Now, in fact, we can find the standard deviation using the STANDARDEVAL.G function, in the value of which we need to enter the sales of the product for each period. The result is a formula of the following form: =STANDARD DEVIATION.Г(C4;D4;E4).
Well, half the work is done. The next step is to form “Variation”, this is obtained by dividing by the average value, standard deviation and converting the result into percentages. We get the following table:
Well, the basic calculations are completed, all that remains is to figure out whether sales are stable or not. Let’s take as a condition that deviations of 10% are considered stable, from 10 to 25% are small deviations, but anything above 25% is no longer stable. To obtain the result according to the conditions, we will use a logical one and to obtain the result we will write the formula:

IF(H4<0,1;"стабильно";ЕСЛИ(H4<0,25;"нормально";"не стабильно"))

All ranges are taken for clarity; your tasks may have completely different conditions.
To improve data visualization, when your table has thousands of positions, you should take advantage of the opportunity to apply certain conditions that you need or use to highlight certain options with a color scheme; this will be very clear.

First, select the ones for which you will apply conditional formatting. In the “Home” control panel, select “Conditional Formatting” and in the drop-down menu, select “Rules for highlighting cells” and then click the menu item “Text contains...”. A dialog box appears in which you enter your conditions.

After you have written down the conditions, for example, “stable” - green, “normal” - yellow and “unstable” - red, we get a beautiful and understandable table in which you can see what to pay attention to first.

Using VBA for the STDEV.Y function

Anyone interested can automate their calculations using macros and use the following function:

Function MyStDevP(Arr) Dim x, aCnt&, aSum#, aAver#, tmp# For Each x In Arr aSum = aSum + x "calculate the sum of the array elements aCnt = aCnt + 1 "calculate the number of elements Next x aAver = aSum / aCnt "average value For Each x In Arr tmp = tmp + (x - aAver) ^ 2 "calculate the sum of the squares of the difference between the array elements and the average value Next x MyStDevP = Sqr(tmp / aCnt) "calculate STANDARDEV.G() End Function

Function MyStDevP(Arr) Dim x , aCnt & , aSum #, aAver#, tmp# For Each x In Arr aSum = aSum + x "calculate the sum of the array elements

In this article I will talk about how to find standard deviation. This material is extremely important for a full understanding of mathematics, so a math tutor should devote a separate lesson or even several to studying it. In this article you will find a link to a detailed and understandable video tutorial that explains what standard deviation is and how to find it.

Standard deviation makes it possible to evaluate the spread of values ​​obtained as a result of measuring a certain parameter. Indicated by the symbol (Greek letter "sigma").

The formula for calculation is quite simple. To find the standard deviation, you need to take the square root of the variance. So now you have to ask, “What is variance?”

What is variance

The definition of variance goes like this. Dispersion is the arithmetic mean of the squared deviations of values ​​from the mean.

To find the variance, perform the following calculations sequentially:

• Determine the average (simple arithmetic average of a series of values).
• Then subtract the average from each value and square the resulting difference (you get squared difference).
• The next step is to calculate the arithmetic mean of the resulting squared differences (You can find out why exactly the squares are below).

Let's look at an example. Let's say you and your friends decide to measure the height of your dogs (in millimeters). As a result of the measurements, you received the following height measurements (at the withers): 600 mm, 470 mm, 170 mm, 430 mm and 300 mm.

Let's calculate the mean, variance and standard deviation.

First let's find the average value. As you already know, to do this you need to add up all the measured values ​​and divide by the number of measurements. Calculation progress:

Average mm.

So, the average (arithmetic mean) is 394 mm.

Now we need to determine deviation of the height of each dog from the average:

Finally, to calculate variance, we square each of the resulting differences, and then find the arithmetic mean of the results obtained:

Dispersion mm 2 .

Thus, the dispersion is 21704 mm 2.

How to find standard deviation

So how can we now calculate the standard deviation, knowing the variance? As we remember, take the square root of it. That is, the standard deviation is equal to:

Mm (rounded to the nearest whole number in mm).

Using this method, we found that some dogs (for example, Rottweilers) are very large dogs. But there are also very small dogs (for example, dachshunds, but you shouldn’t tell them that).

The most interesting thing is that the standard deviation carries useful information. Now we can show which of the obtained height measurement results are within the interval that we get if we plot the standard deviation from the average (to both sides of it).

That is, using the standard deviation, we obtain a “standard” method that allows us to find out which of the values ​​is normal (statistically average), and which is extraordinarily large or, conversely, small.

What is standard deviation

But... everything will be a little different if we analyze sample data. In our example we considered general population. That is, our 5 dogs were the only dogs in the world that interested us.

But if the data is a sample (values ​​selected from a large population), then the calculations need to be done differently.

If there are values, then:

All other calculations are carried out similarly, including the determination of the average.

For example, if our five dogs are just a sample of the population of dogs (all dogs on the planet), we must divide by 4, not 5, namely:

Sample variance = mm 2.

In this case, the standard deviation for the sample is equal to mm (rounded to the nearest whole number).

We can say that we have made some “correction” in the case where our values ​​are just a small sample.

Note. Why exactly squared differences?

But why do we take exactly the squared differences when calculating the variance? Let's say when measuring some parameter, you received the following set of values: 4; 4; -4; -4. If we simply add the absolute deviations from the mean (differences) together... the negative values ​​cancel out with the positive ones:

.

It turns out that this option is useless. Then maybe it’s worth trying the absolute values ​​of the deviations (that is, the modules of these values)?

At first glance, it turns out well (the resulting value, by the way, is called the mean absolute deviation), but not in all cases. Let's try another example. Let the measurement result in the following set of values: 7; 1; -6; -2. Then the average absolute deviation is:

Wow! Again we got a result of 4, although the differences have a much larger spread.

Now let's see what happens if we square the differences (and then take the square root of their sum).

For the first example it will be:

.

For the second example it will be:

Now it’s a completely different matter! The greater the spread of the differences, the greater the standard deviation... which is what we were aiming for.

In fact, this method uses the same idea as when calculating the distance between points, only applied in a different way.

And from a mathematical point of view, using squares and square roots provides more benefit than we could get from absolute deviation values, making standard deviation applicable to other mathematical problems.

Sergey Valerievich told you how to find the standard deviation

Standard deviation is a classic indicator of variability from descriptive statistics.

Standard Deviation, standard deviation, standard deviation, sample standard deviation (eng. standard deviation, STD, STDev) - a very common indicator of dispersion in descriptive statistics. But, because technical analysis is akin to statistics; this indicator can (and should) be used in technical analysis to detect the degree of dispersion of the price of the analyzed instrument over time. Denoted by the Greek symbol Sigma "σ".

Thanks to Carl Gauss and Pearson for allowing us to use standard deviation.

Using standard deviation in technical analysis, we turn this "dispersion index"" V "volatility indicator“, maintaining the meaning, but changing the terms.

What is standard deviation

But besides the intermediate auxiliary calculations, standard deviation is quite acceptable for independent calculation and applications in technical analysis. As an active reader of our magazine burdock noted, “ I still don’t understand why the standard deviation is not included in the set of standard indicators of domestic dealing centers«.

Really, standard deviation can measure the variability of an instrument in a classic and “pure” way. But unfortunately, this indicator is not so common in securities analysis.

Applying standard deviation

Manually calculating the standard deviation is not very interesting, but useful for experience. Standard deviation can be expressed formula STD=√[(∑(x-x ) 2)/n] , which sounds like the root of the sum of the squares of the differences between the elements of the sample and the mean, divided by the number of elements in the sample.

If the number of elements in the sample exceeds 30, then the denominator of the fraction under the root takes the value n-1. Otherwise n is used.

Step by step standard deviation calculation:

1. calculate the arithmetic mean of the data sample
2. subtract this average from each sample element
3. we square all the resulting differences
4. sum up all the resulting squares
5. divide the resulting amount by the number of elements in the sample (or by n-1, if n>30)
6. calculate the square root of the resulting quotient (called dispersion)

One of the main tools statistical analysis is the calculation of the standard deviation. This indicator allows you to estimate the standard deviation for a sample or for a population. Let's learn how to use the standard deviation formula in Excel.

Let’s immediately determine what the standard deviation is and what its formula looks like. This value is the square root of the average arithmetic number squares of the difference between all values ​​of the series and their arithmetic mean. There is an identical name this indicator— standard deviation. Both names are completely equivalent.

But, naturally, in Excel the user does not have to calculate this, since the program does everything for him. Let's learn how to calculate standard deviation in Excel.

Calculation in Excel

You can calculate the specified value in Excel using two special functions STDEV.V(based on the sample population) and STDEV.G(based on the general population). The principle of their operation is absolutely the same, but they can be called in three ways, which we will discuss below.

Method 1: Function Wizard

Method 2: Formulas Tab

Method 3: Manually entering the formula

There is also a way in which you won't need to call the arguments window at all. To do this, you must enter the formula manually.

As you can see, the mechanism for calculating standard deviation in Excel is very simple. The user only needs to enter numbers from the population or references to the cells that contain them. All calculations are performed by the program itself. It is much more difficult to understand what the calculated indicator is and how the calculation results can be applied in practice. But understanding this already relates more to the field of statistics than to learning to work with software.

The coefficient of variation is a comparison of the dispersion of two random values. Quantities have units of measurement, which leads to a comparable result. This coefficient is needed to prepare statistical analysis.

With it, investors can calculate risk indicators before making investments in selected assets. It is useful when the selected assets have different returns and degrees of risk. For example, one asset may have a high income and a high degree of risk, while another, on the contrary, may have a low income and a correspondingly lower degree of risk.

Standard Deviation Calculation

Standard deviation is a statistical value. By calculating this value, the user will receive information about how much the data deviates in one direction or another relative to the average value. Standard deviation in Excel is calculated in several steps.

Prepare data: open the page where the calculations will take place. In our case, this is a picture, but it could be any other file. The main thing is to collect the information that you will use in the table for the calculation.

Enter data into any spreadsheet editor (in our case Excel), filling out the cells from left to right. Should start from column "A". Enter headings in the line at the top, and names in the same columns that relate to headings, only below. Then the date and data to be calculated to the right of the date.

Save this document.

Now let's move on to the calculation itself. Select a cell with the cursor after the last value entered below.

Enter the “=” sign and enter the formula below. The equal sign is required. Otherwise, the program will not calculate the proposed data. The formula is entered without spaces.

The utility will display the names of several formulas. Select " STANDARD DEVIATION" This is the formula for calculating standard deviation. There are two types of calculation:

• with sample calculation;
• with calculation based on the general population.

By selecting one of them, specify the data range. The entire entered formula will look like this: “=STDEV (B2: B5).”

Then click on the button “ Enter" The received data will appear in the marked item.

Calculation of the arithmetic mean

Calculated when the user needs to create a report, for example, by wages in his company. This is done as follows:

• there will only be select range and click on the “Enter” button. And the cell will now display the result from the data taken above.

Calculation of coefficient of variation

Formula for calculating the coefficient of variation:

V= S/X, where S is the standard deviation and X is the average.

In order to calculate the coefficient of variation in Excel, you need to find the standard deviation and the arithmetic mean. That is, having completed the first two calculations, which were shown above, you can move on to working on the coefficient of variation.

To do this, open Excel, fill out two fields where you should enter the resulting numbers of standard deviation and average value.

Now select the cell that is allocated for the number to calculate the variation. Open the tab " Home"if it is not open. Click on the tool " Number" Select percentage format.

Go to the marked cell and double-click on it. Then enter the equal sign and highlight the item where the total standard deviation is entered. Then click on the “slash” or “split” button on your keyboard (looks like this: “/”). Select the item, where the arithmetic mean is entered, and click on the “Enter” button. It should look like this:

And here is the result after pressing “Enter”:

You can also use to calculate the coefficient of variation online calculators, for example planetcalc.ru and allcalc.ru. It is enough to enter the necessary numbers and start the calculation, after which you will receive the necessary information.

Standard deviation

Standard deviation in Excel is solved using two formulas:

In simple words, the root of the variance is extracted. How to calculate variance is discussed below.

The standard deviation is synonymous with the standard deviation and is calculated exactly as well. The cell for the result under the numbers that need to be calculated is highlighted. One of the functions shown in the figure above is inserted. The button “ is clicked Enter" The result has been received.

Oscillation coefficient

The ratio of the range of variation to the average is called the oscillation coefficient. There are no ready-made formulas in Excel, so need to be assembled several functions into one.

The functions that need to be put together are the average, maximum and minimum formulas. This coefficient is used to compare a set of data.

Dispersion

Variance is a function by which characterize the spread of data around mathematical expectation. Calculated using the following equation:

The variables take the following values:

Excel has two functions that determine variance:

To make a calculation, a cell is highlighted under the numbers that need to be calculated. Go to the insert function tab. Select category " Statistical" Select one of the functions from the drop-down list and click on the “Enter” button.

Maximum and minimum

The maximum and minimum are needed so as not to manually search among large quantity numbers minimum or maximum number.

To calculate the maximum, select the entire range required numbers in the table and a separate cell, then click on the “Σ” or “ Autosum" In the window that appears, select “Maximum” and by pressing the “Enter” button you get the desired value.

You do the same thing to get the minimum. Just select the “Minimum” function.