# What makes the standard deviation helpful in the calculation

## Variance

The **Variance** is one of the most important **Dispersion parameters** in the **statistics**. Find out how the **Variance defined** is what value it describes and what the **Difference from the standard deviation** is.

With our** Video **do you understand the topic without any problems - lean back and let ‘explain it to you! What are you waiting for?

You want to understand how exactly the **Calculate variance** leaves or what the **Standard deviation **is? Then take a look at our separate article! Also on the topic **Empirical variance ** we have a contribution.

### Variance explained simply

Finding the variance for the distribution of a random variable (population variance) is easier when you understand what it means. Let's first look at how it is defined.

The variance is the mean squared deviation of all values in a random experiment from their expected value. The formula for the variance is:

You practically estimate how far the individual values of the random experiment are from the expected value. Then you square the deviation. The whole thing is best illustrated graphically. In this context is also the **Standard deviation ** important. It is the root of the variance. Another important distinction is whether it is the variance of a random variable (i.e. the corresponding probability distribution is known) or whether it is a sample (the probability distribution is unknown). In the latter case you have to use the **Sample variance ** to calculate.

### Variance example

Is that too abstract for you? Then imagine the following example:

You have two different games of chance: With the first you can either win or lose € 100 with the same probability, with the second you win exactly one euro or lose one euro. Although both games of chance have exactly the same expected value, namely 0, their variance is very different. This is because the possible results are differently far from the expected value.

### Calculate variance

There is a simple procedure to calculate the variance: First you have to determine the expected value, then insert the individual values in the formula and then calculate the variance. In our article **Calculate variance ** let's go into more detail about the procedure and the formula of the variance.

In this example we can easily determine the variance: First we need the expected value. In both cases it is 0. You calculate this by calculating the individual values times their probability of occurrence and adding them together. If you are unsure how to come up with it, have a look at our **Video on the expected value ** at. Then we can insert the values into the formula for the variance and get two different values of the variance for our game of chance:

Bank note:

Coin:

So you see: Although the expected value is the same, the variance can be very different. This is because the possible events, in the case of the bank note, are further away from the expected value than in the case of the coin.

### Variance in statistics

The variance is a measure of statistics and stochastics, which the **Spread of the data around the mean** indicates. Since there is a difference in the formula, it can only be calculated for cardinally scaled data. You can also tell from the formula that the values are squared, which makes it difficult to interpret. Therefore, the standard deviation is usually used to interpret the spread of the data. If you do not know the probability of occurrence for the events, we will use the sample variance. This weights the individual values equally and forms a distorted or undistorted estimator of the variance. If you want to learn more about it, check out our article **Sample variance ** at!

### Difference variance standard deviation

So if we want to interpret the dispersion around the mean, it is not so easy to do with the variance. Instead, we can do the **Standard deviation **use. But what is the difference between these two values?

The standard deviation is the square root of the variance

You can see from the formula: The standard deviation is nothing other than the root of the variance. Based on our example, we get a standard deviation of € 100 and € 1 - this is how far the values are on average from the mean.

In order to be able to compare individual random experiments with one another and to be able to interpret the values better, it is therefore often helpful to calculate the standard deviation.

- How does Bitcoin work in Nigeria
- What is today's hour of life
- Excursions help students learn better
- What is 56 87 25
- Interaction is required for juniors
- What's your rating on EktaTech Company
- What comes after 5 25 61 116
- What are surface coils in the MRI
- Why DC is given to start the transistor
- What is a domain registration

- How feasible is this IB timetable
- Why do birds chirp when they are threatened
- SEOMoz vs SEOprofiler
- What's your favorite moment for Severus Snape
- How do grocery stores wash fresh vegetables
- What is the leanest type of meat
- What is the Dallas Cowboys playoff history
- Do liberals realize that most bankrupts are liberals
- Whose cell was discovered
- Do you like change
- Who is Katherine Jackson
- What is a Napoleon Complex in Psychology
- Which AIIMS is better Bhopal or Nagpur
- What is spatial domain in image processing
- Christians eat pork
- Does the headset damage the ear?
- Are Ricky and Morty the same person
- What is Urbex Photography
- What is the oldest winery in France
- Is it uncomfortable to wear condoms?
- What is the future of underwater technology?
- How do you construct this function
- What is a mere duct in the air conditioning system
- Unattended feature learning really works