 # Difference Between Variance and Standard Deviation

Knowledge of mathematical terms helps to solve the problems quickly. Here in this article, you will study the difference between standard deviation and variance. In statistical problems, both terms are utilized as metrics. Well, these methods are used explicitly in accounting, business, and finance. If you are not aware of mean and range dispersion measures, it is advisable to know to revise them first. Here we have also explained the relation of variance and standard deviation. So, before knowing the difference in variance and standard deviation, both metrics' terms, let us understand the standard deviation definition and variance definition.

### Variance Definition

Variance is referred to as the variability measure to represent the members of the group. It is the distance of observations corresponding to a higher variance value. It is a squared measure.

Variance is either zero or positive but never negative because of the squared value.

### Variance Formula

σ2 = ∑ (x – M)2/n

M=mean

X= value of data set

N= number of observations in the given data set

### Standard Deviation Definition

A straightforward dispersion measure is the standard deviation. Also, it defines the method of data value spread around the mean in a data set. We can refer to it as the closeness between the data set values and mean.

The standard deviation always measures according to the original data, and it is still positive.

### Standard Deviation Formula

σ = √∑ (x – M)2/n

M=mean

X= value of data set

N= number of observations in the given data set

### Key Differences Between Variance And Standard Deviation

It is essential to know the definition and understand the basic concepts whenever you need to differentiate two terms in any subject. Here we have differentiated both the measures.

### Variance

Variance is a numeric value, and it is a squared value. It defines the variability of observations.

The average value of squared deviation is referred to as variance.

Its value is always squared.

Denominate as (σ2) in mathematics

It is the individual data spread out indicator in a group

### Standard Deviation

Measured observations that are the result of measuring by dispersion in the given data set are standard deviation.

It is merely the root square value of the mean square deviation

The unit is derived from the group of original data only.

Denominates as (σ) in mathematics

It is referred to as observations' perfect indicator in the available data set.

### Applications

The variance combines all the values during a set of knowledge to quantify the measure of spread. The more prominent the range, the more the variation ends during a more significant gap between the values within the data set. Variance is primarily used for the statistical probability distribution of living volatility from the mean, and volatility is among the measures of risk analysis, which could help investors work out the danger in investment portfolios. it's also one of the critical aspects of asset allocation. On the other hand, the variance is often utilized in a good range of applications like in the finance sector as a measure of market and security volatility. Also, dog route, class strength, weather prediction, class-wise students' appearance in exams, department- careful salary checking, and market researches need these values.

### Relation: Standard Deviation And Variance?

Standard deviation is the square root value of that of the variance value.

### Explanation:

Variance

σ2=(1n)⋅Σni=1(xi−¯x)

Standard deviation

σ=√(1n)⋅Σni=1(xi−¯x)

### Example 1:

Marks scored by a student in five subjects are 60, 75, 46, 58, and 80, respectively. You have to find out the standard deviation and variance.

First of all, you have to find out the mean,

Mean= (60+75+46+58+80)/5= 63.8

So the average (mean) marks are 63.8

Now calculate the variance

 X A (X-A) (X-A)^2 60 63.8 -3.8 14.44 75 63.8 11.2 125.44 46 63.8 -17.8 316.84 58 63.8 5.8 33.64 80 63.8 16.2 262.44

Where, X = Observations

A = Arithmetic Mean

Variance= (14.44+125.44+316.84+33.64+262.44)/5 = 150.56

So the variance is 150.56

And Standard deviation is –

σ=square root of 150.56= 12.27

### Similarities

• Both standard deviation and variance are always positive.

• Both values are zero when all the observations are identical.

### Conclusion

Some analysis and decision -making processes need these two values in various sectors. Standard deviation is written with the same standard measure unit as given in the data set. Also, the variance is written with bigger units as it is a square measure.

### Example 2:

Make a list of the height of dogs. You can take the help of neighbours, relatives, and your friends to collect different observations. Remember that you should have the details of the height in mm units.

Suppose heights you may get are 430mm, 170mm, 300mm, and 600mm.

You can make the table or chart as given below to understand the proper observations.

Now, you need to get the values of standard deviation, mean, and variance.

Step1: How to find mean?

Mean =(600 + 470 + 170 + 430 + 3005)  = 19705

Mean = 394

So, the average height of all dogs is 394mm.

Calculation: Each Dog differentiated from the mean value

Calculation: Variance

To calculate variance, let's get the average value of the squared value of data

### Variance

σ2 = 2062 + 762 + (−224)2 + 362 + (−94)25

=(42436 + 5776 + 50176 + 1296 + 88365)

=1085205

Variance= 21704

Therefore, Variance: 21,704

Let's calculate the standard deviation by square rooting the value of variance

### Standard Deviation

σ  = √21704

= 147.32....

= 147 ( to the nearest mm )