Page 198 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Methodology of Social Research

note S fx
formula of arithmetic average =
f
Number of families (∑f) = 735
Sum of number of children in each family (∑fx) = 2166
Sfx
M
\ M = =
Sf
= 2166/735 = 2.9 or 3 children
therefore, arithmetic average of number of children born in every family= 3 children.
(b) Short-cut Method- there are following stages to calculate the arithmetic average using short-cut
method-
(i) firstly we assume any element as the assumed mean in a discrete series and thereafter
calculate the deviation of values of elements from that assumed mean.
(ii) Thereafter the we multiply each frequency with its related deviation and find its sum.
(iii) in this way after dividing the above sum from the sum of frequencies, we get the result. to
this result we add the assumed mean.
(iv) this sum is the arithmetic average.
if assumed mean is A, sum of frequencies is n, and the sum of deviations (d) is assumed as ∑fd then
the above method can be written as a formula in this way-
S fx
M = A +
n
if the symbol n for sum of frequencies is replaced by ∑f then the formula would be like this
S fd
M = A +
f S
in order words,
sum of the multiplication of deviations and frequencies
Mean = Assumed mean +
sum of frequencies

Example 4 Calculate the arithmetic average of the number of children born in each
family as given in example 3 using short-cut method.

Solution: Calculation of the arithmetic average of the number of children born in each family
using short-cut method.

Number of children number of Deviation (d) from
born in each family (x) families (f) assumed mean (a = 6) total deviation (f, d)
0 96 (0 – 6) = – 6 (96 × – 6) = – 576
1 108 (1 – 6) = – 5 (108 × – 5) = – 540
2 154 (2 – 6) = – 4 (154 × – 4) = – 616
3 126 (3 – 6) = – 3 (126 × – 3) = – 378
4 95 (4 – 6) = – 2 (95 × – 2) = – 190
5 62 (5 – 6) = – 1 (62 × – 1) = – 62
6 (A) 45 (6 – 6) = – 0 (45 × 0) = 0

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