Standard Deviation – Evidence for the Formula How to Determine and Example Questions

standard deviation – Standard deviation is a statistical technique often used for interpretation homogeneity Collection. For more details, please refer to our discussion of standard deviation material starting with standard deviation definition, standard deviation formulas, and sample standard deviation problems below.

Define standard deviation

standard deviation It is one of the statistical techniques that are often used in the explanation homogeneity Collection. Standard deviation is a statistical value often used to determine how data is distributed in a sample, as well as how close individual data points are to the mean or mean value of the sample.

There is something we need to know before we discuss the standard deviation equation. The standard deviation of the data set can be = 0 Or even greater or less than zero (0).

  • If the value is zero, then all values ​​in the set become equal.
  • Meanwhile, a value whose value is greater or less indicates that the individual data point is far from its mean value.

If we want to find the value of the standard deviation, the first step we have to do is as follows:

  • First, calculate the average value of each existing data point.
  • The mean value is equal to the sum of all values ​​in the data set
  • We divide by the total number of points from the data.

Not only that, the following steps are:

Then calculate the deviation of each data point from its mean. That is, by subtracting the value from the average value.

Next, we square the deviation for each data point and then find the mean of the individual squared deviation. From the resulting value, which is called fries.

Then, if you want to find the standard deviation, it will be by Take the square root of the variance.

Equation

Here is the formula for standard deviation:

1. Population standard deviation

Population can be denoted by σ (sigma) It can also be defined by the following formula:

2. Sample standard deviation

Model standard deviation, the formula is as follows:

3. Account

Determining the basis for calculating variance is the desire to know the variance of each data set.

So you can find out the variance of the data set, i.e. by decreasing the value of the data along with the mean of the data set, after that, all the results are added up.

It’s just that this method can’t be used anymore because the result will always be 0 (zero).

So, until the result is not 0, what we do is square each data value subtraction and the mean of the data set and then add it up.

In this way, the result of the sum of squares will have a positive value.

The variance value obtained from dividing the sum of squares with the size of the data (n).

However, when the variance value is applied, it is usually used to estimate the variance of a population. Using the above formulas, the value of the content variance will be greater than the variance of the sample.

In order not to be able to predict the population variance, n is used as a divisor of the sum of squares to be replaced by n-1 (degrees of freedom) so that the sample variance value is close to the population variance.

In this way, the formula for the variance model will be:

The obtained variance value is a value in square form.

For example, the unit for the mean value is grams (g) so the value of the variance is grams (g) squared.

In getting the unit value, the variance is again squared so that the result can be a standard deviation.

To simplify the calculation, the formulas for variance and standard deviation can be derived.

4. Variable formula

The variable formula is as follows:

5. Standard deviation formula

The formula for the standard deviation is as follows:

Information :

  • s2 = Varian
  • s = standard deviation
  • xi = value of xi
  • = average
  • n = sample size

An example of a standard deviation problem

Pak Arianto used the height of 10 students in SD Suka Jaya as a sample. Below are the sample data collected by Mr. Ariyanto:

172, 167, 180, 170, 169, 160, 175, 165, 173, 170

Therefore, calculate the standard deviation based on the above problem.

Answer:

It is known that the number of data (n) = 10 and (n -1) = 9. Then you first look for the variance. To facilitate the calculation, you can also arrange a table like the photo below.

Table

From the above table, the next step is to calculate as follows.

Standard deviation of the group data

Then put it in the covariance formula. So it will be as follows:

How to calculate the standard deviation manually

From here we already know that the variance value is 30.32. So, to calculate the standard deviation, you only need the square root of the variance value.

s = -30.32 = 5,51

So, the standard deviation of the above example is 5,51.

What is the standard deviation?

standard deviation It is one of the statistical techniques that are often used in the explanation homogeneity Collection.

Standard deviation formula

Hence our discussion of the standard deviation material. It might be useful.

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