You will need

- Calculator, computer

Instruction

1

Let there be a few numbers that characterize any homogeneous magnitudes. For example, the results of izmereniy, weightings, statistical surveys, etc., All represented values must be measured with the same unit. To find the standard deviation, perform the following steps.

Determine the arithmetic mean of all the numbers: add up the numbers and divide the sum by the total number of numbers.

Determine the arithmetic mean of all the numbers: add up the numbers and divide the sum by the total number of numbers.

2

Find the deviation of each number from its mean value: subtract each number from the arithmetic average calculated in the previous paragraph.

3

Determine the variance (dispersion) of numbers: add together the squares of the deviations found previously and divide the resulting amount by the number of numbers.

4

Extract of the variance square root. The resulting number will be the standard deviation of the given set of numbers.

5

Example.

In the house is based on seven patients with fever 34, 35, 36, 37, 38, 39 and 40 degrees Celsius.

It is required to determine the standard deviation from the average temperature.

Solution:

• "the average temperature in the chamber": (34+35+36+37+38+39+40)/7=37 º C;

• deviations of temperature from the average (in this case the normal value): 34-37, 35-37, 36-37, 37-37, 38-37, 39-37, 40-37, it turns out: -3, -2, -1, 0, 1, 2, 3 (º C);

• dispersion: ((-3)2+(-2)2+(-1)2+02+12+22+32)/7=(9+4+1+0+1+4+9)/7=4 (ºС2);

• standard deviation: √4=2 (°C);

Answer: the average chamber temperature – normal: 37 ° C, but the standard deviation of temperature is 2 ° C, which indicates serious problems in patients.

In the house is based on seven patients with fever 34, 35, 36, 37, 38, 39 and 40 degrees Celsius.

It is required to determine the standard deviation from the average temperature.

Solution:

• "the average temperature in the chamber": (34+35+36+37+38+39+40)/7=37 º C;

• deviations of temperature from the average (in this case the normal value): 34-37, 35-37, 36-37, 37-37, 38-37, 39-37, 40-37, it turns out: -3, -2, -1, 0, 1, 2, 3 (º C);

• dispersion: ((-3)2+(-2)2+(-1)2+02+12+22+32)/7=(9+4+1+0+1+4+9)/7=4 (ºС2);

• standard deviation: √4=2 (°C);

Answer: the average chamber temperature – normal: 37 ° C, but the standard deviation of temperature is 2 ° C, which indicates serious problems in patients.

6

If there is a possibility to use the program Excel, the calculation of the variance, respectively, and standard deviation can be significantly simplified.

To do this, place the measurement data in one row (one column) and use an aggregate function VARP. As the function arguments specify the range of cells of the table where you placed the entered number.

To do this, place the measurement data in one row (one column) and use an aggregate function VARP. As the function arguments specify the range of cells of the table where you placed the entered number.

# Advice 2: How to calculate arithmetic mean

**The average**value is one of the characteristics of a set of numbers. Is a number that cannot go beyond the range defined by the largest and smallest values in this set of numbers.

**The average**arithmetic value is the most commonly used kind of average.

Instruction

1

Add up all numbers and divide them by the number of terms to obtain the arithmetic mean. Depending on the specific conditions of calculations it is sometimes easier to divide each number by the number of a data set and sum the result.

2

Use, for example, included in the Windows calculator, if you calculate the average arithmetic value in mind is not possible. You can open it using run dialog programs. To do this, press the "hot keys" WIN + R or click start and select in the main menu the command "Run". Then type in the input box and press calc on the keypad Enter or click "OK". The same can be done via main menu - open it, go to "All programs" and in "Standard" and select "Calculator".

3

Enter the sequence number of the set, clicking on the keyboard after each one (except the last) the "Plus" key or by clicking the appropriate button in the calculator interface. To enter the numbers too as you can with the keyboard or clicking the appropriate button interface.

4

Press the slash (slash), or click the icon in the interface of the calculator after entering the last value sets and print the number of numbers in the sequence. Then press the equal sign and the calculator will calculate and display the arithmetic mean value.

5

It is possible for this purpose to use the table editor Microsoft Excel. In this case, run the editor and enter in the adjacent cell all values of the sequence numbers. If after entering each number, you press Enter or the down arrow key or the right, the editor will move the input focus into the next cell.

6

Select all entries and in the lower left corner of the editor window (in the status) will see the average value for the selected cells.

7

Click the following for the last entered number cell, if you do not enough only to see the arithmetical mean value. Open the drop-down list with the image of the Greek letter Sigma (Σ) in the group of commands "Edit" on the Home tab. Select the line "

**Average**" and the editor will insert the correct formula to calculate the arithmetic mean of the values in the selected cell. Press Enter and the value will be calculated.# Advice 3: How to find average and variance

The calculation of the average is one of the most common methods of generalization. The average reflects all things in common, which is typical for the characteristics of the aggregate. But at the same time, he ignores the differences of the individual units.

Instruction

1

The most common in the calculation is a simple average. You can easily find if there is a set of two or more statistical indicators, arranged in any order. Simple arithmetic average is defined as the ratio of the sum of the individual values of the attribute to the number of features in combination: Khsr = ?XI/n.

2

If the volume of the aggregate is large and represents the number distribution, the calculation must use the weighted arithmetic mean. This way you can determine, for example, the average price per unit: total value of products (product of the number of each type in the price) are divided by the total volume of products: Khsr = ?XI*fi/?fi. In other words a weighted average is defined as the ratio of sums of products of characteristic values and the frequency of repetition of the sign of the sum of the frequencies of all features. It is used in cases where the options researched population occur different number of times.

3

In some cases you need to apply in the calculation of the average harmonic. It is used when you know the individual characteristic values x and fx work, and the value of f is not known: Khsr = ?wi/?(wi/XI), where wi = XI*fi. If the individual characteristic values meet once (all wi =1), the harmonic average is applied is simple: Khsr = N/?(wi/XI).

4

**The variance**you can calculate as follows: D = ?(X-Khsr)^2/N, in other words the variance is the average squared deviation from the mean value. There is another way of calculating this indicator: D = (X^2)CP – (Khsr)^2.

**The variance**difficult to interpret meaningful. However, the square root of it characterizes standard deviation. It reflects the average deviation of the characteristic from the average value of the sample.