Page 1 - Lession note - stat chap -9,MCT (AM)-49

Class-XI

STATISICS

CHAPTER-Measures of Central Tendency

Topic –Arithmetic Mean (Module-49)

Continuous 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 group data and frequency i.e that is
dealing with group frequency distribution series .
Can be calculated under three heads -

 Direct Method According to this method, we find the Arithmetic mean from the
following formula
= ∑fm / ∑f , = Arithmetic Mean, ∑fm = Sum of all values /items(m =
mid values ) 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 ,where d = X-M
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 ,Using three methods
X 0-5 5-10 10-15 15-20 20-25
f 2 3 4 3 2