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| What is the variance in statistics |
"What is the variance in statistics", Variance is one of the measures that could be used to determine if there are any significant differences between the means of two or more different populations.
What is the variance in statistics
When you are looking at a random variable and wonder how much it varies from its mean, variance can help.
For example, let's say you have a population of people with their age and income. You can see that the average person and the richest person tends to earn $72,000 compared to the average person and poor person. If we look at the actual population, the mean would be as high as $72,000 and the wealthiest people would earn more than other.
Now let's assume that we are able to measure each person's income by using standardized income. In our case, we can measure by income in different categories like education, marital status, job title, etc. For example, let's say you only measure an individual's salary by standardized income. Then when you have collected all variables of your people, you get a total variance of each individual and each category. We can then estimate their overall income of each person.
What is the definition of variance?
The standard deviation is a measure of variability of any given data set. It measures what differs among the values of a certain parameter in your data set such as income.
Standard deviation formula
The standard deviation formula is
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| What is the variance in statistics |
It measures how far from a central value it has. It helps us understand what different groups are doing on average. Here we can see that most of the group earn less than their group mean income.
Let's take a look at another example. Suppose that we have 100 students from class A and class B respectively. So the mean income of students from both classes would be $90,000. But if we can measure the students' income by standardized income then we can calculate their standard deviations thus finding out how much income they earn.
But not everyone knows about this, so let's discuss what we need to know next.
What is the calculation behind variance?
In order to calculate standard deviation, calculate two things — mean and deviation. These two variables will help us form the standard deviation formula. The formula for calculating standard deviation is
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| What is the variance in statistics |
Squaring deviation with respect to mean
Standard deviation is calculated by subtracting the mean from each of the variables. When we subtract the mean from each variable, we divide it by the square root of the number of variance. Each variance can have negative or positive value and we divide the square root by the number of variance.
Now we calculate standard deviation in the following example
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| What is the variance in statistics |
The main reason behind this is that we don't want to count every time we divide one of our variables by our standard deviation, then because the standard deviation is a percentage, our variation can go up or down. Now, the easiest way to handle such scenario is to just count it once and we already know it will increase.
So we need to do something to prevent that thing, we already know that it will raise our standard deviation.
What is variance coefficient?
The variance coefficient is the statistical measure of average variations or changes between sample means and the standard ones.
Variance coefficient formula
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| What is the variance in statistics |
We can apply to variance coefficients to calculate individual variables as well as for comparing them against each other.
From the above example of mean and standard deviation.
Mean = 4, S.D = 2.16
C.V = 2.16/4
= 0.54
What is the significance of variance?
It is the likelihood of the observed data following a normal distribution.
Statisticians use this term when they are trying to draw a conclusion about their results. It is used to describe the probability that the observations were generated by random processes rather than by some real-life process such as income or employment.
Now let's talk about variance ratios.
Variance ratio
It is an estimate of the proportion of variance between each variable in the group. The higher the ratio the greater variance, the lower is it the smaller the variance and vice versa. The larger the ratio the lesser is the variance. Basically, the larger the variance, the better it is to predict the future outcome.
Variance ratio formula
Variance ratios can be computed in the same way but it calculates the variances separately for different variables and compares these variances to determine variances for each group at that time.
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