the algebraic sum of the deviations of a frequency distribution from its mean is..

a. always+ve

b. always-ve

c. 0

d. a non-zero number..

plz answer....and also giv de reason for ur answer..plz!!!!

The algebraic sum of the deviations of a frequency distribution from its mean is zero.
You can understand it by the following example,
 

Consider the following distribution of daily wages of 50 worker of a factory.

Daily wages (in Rs)

100­ − 120

120­ − 140

140 −1 60

160 − 180

180 − 200

Number of workers

12

14

8

6

10

Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer :
 

To find the class mark for each interval, the following relation is used.

Class size (h) of this data = 20

Taking 150 as assured mean (a), diui, and fiui can be calculated as follows.

Daily wages

(in Rs)

Number of workers (fi)

xi

di = xi − 150

fiui

100­ −120

12

110

− 40

− 2

− 24

120­ − 140

14

130

− 20

− 1

− 14

140 − 160

8

150

0

0

0

160 −180

6

170

20

1

6

180 − 200

10

190

40

2

20

Total

50

     

− 12


Here, we can see that entries in column di represent deviations from the mean, and if sum them together, the result comes out to be 0. Hence, the desired answer.

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