Page 196 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Methodology of Social Research

note formula of calculation of arithmetic average (M) by short-cut method—
S d
M = A +
n
Here assumed mean A = 160
Sd = 30
n = 10 (because there are 10 students)
30
M = 160 +
10
= 160 + 3 = 163
therefore, the arithmetic average of 10 students = 163 cms

Notes Here one thing should be noticed that the solution obtained from the direct method
and the short-cut method should be same as in example 1 and 2.

self assessment
fill in the blanks:
1. the calculation of arithmetic average is in reality ______________that is taught to students
in lower classes.
2. the result obtained by dividing is known as ___________
3. If we know the _____________ and number of elements then we can find out the real sum.

27.4 calculation of Mean in Discrete series

(a) Direct Method–Arithmetic average is calculated in the condition when the elements are in distinct
categories. in such a situation the technique to calculate the mean has following stages-
(i) Multiply each frequency with its value.
(ii) this way calculate the sum of all multiplications
(iii) Divide this from the sum of frequencies
(iv) the result obtained is called as mean.
this technique can be demonstrated with the help of a formula using various symbols:
if we assume that-
Value of an element = x
frequency = f
Value of an element × frequency = fx
Sum of frequency = ∑f
Sum of (Value of an element × frequency) = ∑fx
then according to above method-
M = ∑fx/∑f
Sum of (Value of an element frequency)
×
therefore mean (M) =
sum of frequency

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