Page 1 - Lession note - stat chap -9,MCT (AM)-48

Class-XI

STATISICS

CHAPTER-Measures of Central Tendency

Topic –Arithmetic Mean (Module-48)

Discrete series

Short note

Arithmetic Mean
Arithmetic Mean is the number which is obtained by adding the values of

all the items of a series and dividing the total by the number of items.

This series is associated with frequency i.e that is dealing with frequency
distribution series .
Can be calculated under three heads -

 Direct Method According to this method, we find the Arithmetic mean from the
following formula
= ∑fX / ∑f , = Arithmetic Mean, ∑fX = Sum of all values /items
multiplied with respective frequency , ∑f =N= Sum of frequencies

 Short-cut Method By short cut method, we find the Arithmetic Mean from the
following formula
= A+∑fd / ∑f d= X-A
Here, = Arithmetic Mean, A = Assumed average , ∑fd = Net sum of the
deviations of the different values from the assumed average multiplied with
respective frequency; and N= ∑f = Number of items in the series,

 Step deviation method , = A+ (sum of fd / ∑f)*c ,where d = d/c ,
1
1
1
= Arithmetic Mean, A = Assumed average ,Efd = Net sum of the deviations of
the different values from the assumed average multiplied with respective
frequency; and Ef = Number of items in the series,

Examples:- Find the AM of the following values ,through three methods

X 2 4 6 4 2
f 3 2 1 2 3