III. The algebric sum of the deviations of
20observations measured from 30 is 2.
The mean of these observations is c.
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Answer:
Let the 20 deviations be a
1
,a
2
,...,a
20
Therefore the observations are (30+a
1
),(30+a
2
),...,(30+a
20
)
Given that sum of the deviations is 2
Therefore, a
1
+a
2
+...+a
20
=2 ------(1)
Hence, mean=
20
(30+a
1
)+(30+a
2
)+...+(30+a
20
)
⟹mean=
20
a
1
+a
2
+...+a
20
+20(30)
⟹mean=
20
2+20(30)
(from (1))
⟹mean=
20
602
=30.1
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