Mathematics
If M is the mean of six natural numbers x1, x2, x3, x4, x5 and x6. Show that :
(x1 - M) + (x2 - M) + (x3 - M) + (x4 - M) + (x5 - M) + (x6 - M) = 0
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Answer
Given,
M is the mean of six natural numbers x1, x2, x3, x4, x5 and x6.
= M
⇒ x1 + x2 + x3 + x4 + x5 + x6 = 6M
⇒ x1 + x2 + x3 + x4 + x5 + x6 = M + M + M + M + M + M
⇒ (x1 - M) + (x2 - M) + (x3 - M) + (x4 - M) + (x5 - M) + (x6 - M) = 0
Hence, proved that (x1 - M) + (x2 - M) + (x3 - M) + (x4 - M) + (x5 - M) + (x6 - M) = 0.
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