Question

What are the advantages and disadvantages of standard deviation?

Answer 1

Hint : To discuss the advantages and disadvantages of standard deviation, first, we need to know what is standard deviation.
Standard deviation helps us to determine the dispersion from the given mean.
Dispersion means it is the value by which an object differs from another object, in this type of particular case it is also known as the arithmetic mean.
Standard deviation denotes the typical deviation from the given mean.
Mean is the average from the given, or also known as the sum of the numbers divides the total number in the given.



Complete step-by-step solution:
Advantages: the standard deviation advantages are
In standard deviation the given values are always fixed and also the rigidification (extracting way) is well defined.
In standard deviation, mathematical operations like addition, subtraction, multiplication, division, and statistical analysis, both are possible with the use of standard deviation.
It shows exactly how much of the given data are clustered around the given mean.
Disadvantages: the standard deviation disadvantages are
It will affect the extreme values in the standard deviation.
The open-end frequency distribution is calculated using the standard deviation.
The standard deviation does not give the full range of the given data.
It was hard to calculate.
The formula of the standard deviation is $\sigma = \sqrt {\dfrac{{\sum\limits_{i = 1}^n {{{(xi - \overline x )}^2}} }}{{n - 1}}} $, where $\sigma $is denoted as the sigma, $\overline x $indicates the mean of the given values, n is the total number of values from the given.

Note:Steps to calculate the standard deviation
By adding the given all data points and dividing them by the number of given data points, we can obtain the mean.
By subtraction of the given values from the data of the mean, you can get the variance for each of the points. Next, we need to square the obtained values and sum the required results.
After that, we need to divide the results obtained by the number of data points.
Finally, take the square root of the variance from the above step. And the resulting value is the standard deviation.