Question

What is the meaning of the term deviation?

Answer 1

Hint: We use concepts related to statistics to solve this problem, and you will know about the terms related to, in detail. We can also find the mean of a given set of observations using this deviation method also. We will also know about some methods of finding central tendencies.

Complete step by step solution:
In statistics, a given set of numbers are called observations.
Let the observations be $$x_1,x_2,x_3,.....x_n$$ . So, we have $$n$$ observations here.
There are three ways to measure the central tendency of given observations. They are “mean”, “median”, and “mode”.
Firstly, the mean is equal to the sum of observations divided by number of observations. And represented by $$\bar{x}$$ .
So, $$mean=\bar{x}={\displaystyle \frac{x_1+x_2+x_3+......+x_n}{n}}$$
And median is equal to, $${\left({\displaystyle \frac{n+1}{2}}\right)}^{th}$$ term if $$n$$ is odd or is equal to average of $${\left({\displaystyle \frac{n}{2}}\right)}^{th}$$ term and $${\left({\displaystyle \frac{n}{2}}+1\right)}^{th}$$ term.
And mode is equal to the observation which is repeated the most.
And now, deviation is defined as a measure of difference between the observed value of a variable (often it is either mean or median or mode) and other values.
So, $$D_i=|x_i-m(X)|$$
Where $$m(X)$$ is either mean or median or mode.
And, $$D_i$$ is an absolute deviation which is an individual one for individual observations.
And, $$x_i$$ is an element of observation.
And mean deviation is known as mean value of deviations.
That means, all deviations are considered as new observations and mean is calculated.
$$\text{Mean deviation = }{\displaystyle \frac{1}{n}}\sum _{i=1}^n|D_i-m(X)|$$
So, we can find mean deviations in this way.

Note: While taking deviations, we consider the modulus of it. Which means, we have to consider the positive value only in any condition i.e. if we get a positive value, then we consider positive, and if we get a negative value, then also we should consider a positive value.