Imply is likely one of the commonest measure of central tendency. For assortment of numbers, it represents the middle level within the assortment. Additionally it is referred to as Common or Anticipated worth and represented by “μ”.
Let’s imagine the datapoints in a set is given as [x₁, x₂, x₃, …. xₙ]
the place:-
xᵢ : represents datapoint at i^th place
n : represents whole variety of datapoints
μ = (x₁+ x₂ + x₃ + …. + xₙ)/n = 𝛴x/n
For instance :-
In a category a gaggle of 5 college students have scored 50, 80, 92, 98 and 33. The imply of their scores shall be
μ = (50+80+92+98+33)/5 = 70.6
- Imply signifies a area the place most values within the distribution fall and referred as central location of distribution
- We are able to additionally consider it as center level among the many statement
- Imply could be very delicate to outliers within the dataset and fails to accurately measure the central tendency within the presence of outliers
- Additionally they fail if the info is skewed in a single route
Lets take an instance:-
Within the following graph
x-axis : represents marks scored by college students
y-axis : variety of college students scored the marks
Within the above instance, common of give knowledge is 77.41 which doesn’t point out the central tendency because the outliers are pushing the imply away from the central level.
Because the distribution turns into extra skewed, the imply is drawn additional away from the middle
Imply signifies central tendency solely when we’ve got symmetric distribution