Arithmetic Mean formula
Arithmetic mean formula:In general language arithmetic mean is same as the average of data and it is the representative value of the group of data. Suppose we are given ‘ n ‘ number of data and we need to compute the arithmetic mean, all that we need to do is just sum up all the numbers and divide it by the total numbers.
Arithmetic Mean Definition
Arithmetic mean represents a number that is obtained by dividing the sum of the elements of a set by the number of values in the set. So,you can use the layman term Average, or be a little bit fancier and use the word “Arithmetic mean” your call, take your pick -they both mean the same. The arithmetic mean may be either
- Simple Arithmetic Mean
- Weighted Arithmetic Mean
Arithmetic Mean Formula
If any data set consisting of the values b1, b2, b3, …., bn then the arithmetic mean B is defined as: so.
B = (Sum of all observations)/ (Total number of observation)
= 1/n ∑ni=1bi=b1+b2+b3+….+bnn
If these n observations have corresponding frequencies, the arithmetic mean is computed using the formula
x = x1f1+x2f2+……+xnfnN and
using Sigma notation = ∑ni=1xifiN
where N = f1+ f2 + ……….+ fn.
The above formula can also be used to find the weighted arithmetic mean by taking f1, f2,…., fn as the weights of x1, x2,….., xn.
When the frequencies divided by N are replaced by probabilities p1, p2, ……,pn we get the formula for the expected value of a discrete random variable.
X = x1p1 + x2p2 +…….+ xnpn. or
using Sigma notation = ∑ni=1xipi
then the formula=x = x1f1+x2f2+……+xnfnN.