Page 203 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Unit-27: Measures of Central Tendency: Mean, Median, Mode

note
Example 7 Calculate the arithmetic average using short-cut method for the data given
below for the production of crop.

Production 0.5 – 4.5 4.5 – 8.5 8.5 – 12.5 12.5 – 16.5 16.5 – 20.5 20.5 – 24.5
Number of 4 8 5 10 8 9
farms
solution: We need to prepare the given below table to solve the above question using the facts
given:
table 27.5
production number Mean of Deviation Multiplication
of farms production class– (a=10.5) of mean of deviation and
(f) intervals from (x–A)=d numbers of farms
(x) (fd)

 + 4.5  0.5
0.5–4.5 4   = 2.5 (2.5–10.5) = – 8 (8 × – 4) = – 32
 2 
 4.5 + 8.5 
4.5–8.5 8   = 6.5 (6.5–10.5) = – 4 (8 × – 4) = – 32
 2 

 8.5 + 12.5 
8.5–12.5 5   = 10.5 (10.5–10.5) = 0 (5 × 0) = 0
 2 
 + 16.5  12.5
12.5–16.5 10   = 14.5 (14.5–10.5) = + 4 (10 × 4) = + 40
 2 
 + 20.5  16.5
16.5–20.5 8   = 18.5 (18.5–10.5) = + 8 (8 × 8) = + 64
 2 

 20.5 + 24.5 
20.5–24.5 9   = 22.5 (22.5–10.5) = + 12 (9 × 12) = + 108
 2 
S f means S fd = (212–64) n = 44
= + 148
formula for calculating arithmetic average using short-cut method or step deviation method—
S f d S f d
M = A + or A +
S f S n
Here assumed mean (A)= 10.5
S fd = + 148
S f or n = 44 (number of farms)
148 37
M = 10.5 + = 10.5 + = 10.5 + 3.36
44 11
= 13.86

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