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!!!!
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.
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), di, ui, 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.