Let \(\overline{x}\) be the mean of n observations x1 , x2 , x3 ,...xn

1.	Let \(\overline{x}\) be the mean of n observations x1 , x2 , x3 ,...xn. If (a – b) is added to each observation, then what is the mean of the new set of observations?(a) zero (b) \(\overline{x}\) (c) \(\overline{x}\) – (a – b) (d) \(\overline{x}\) + (a – b)
Answer» (d) \(\overline{x} + (a-b)\) Given, \(\frac{x_1 + x_2+x_3+.....+x_n}{n}=\overline{x}\) ∴ \(\frac{x_1 +(a-b) +x_2+(a - b)+x_3+(a-b)+.....+x_n+(a-b)}{n}\) = \(\frac{x_1 + x_2+x_3+.....+x_n}{n} + \frac{n(a-b)}{n}\) = \(\overline{x} + (a-b)\)

Let \(\overline{x}\) be the mean of n observations x1 , x2 , x3 ,...xn. If (a – b) is added to each observation, then what is the mean of the new set of observations?(a) zero (b) \(\overline{x}\) (c) \(\overline{x}\) – (a – b) (d) \(\overline{x}\) + (a – b)

Answer»

(d) \(\overline{x} + (a-b)\)

Given, \(\frac{x_1 + x_2+x_3+.....+x_n}{n}=\overline{x}\)

∴ \(\frac{x_1 +(a-b) +x_2+(a - b)+x_3+(a-b)+.....+x_n+(a-b)}{n}\)

= \(\frac{x_1 + x_2+x_3+.....+x_n}{n} + \frac{n(a-b)}{n}\)

= \(\overline{x} + (a-b)\)

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Let \(\overline{x}\) be the mean of n observations x1 , x2 , x3 ,...xn. If (a – b) is added to each observation, then what is the mean of the new set of observations?(a) zero (b) \(\overline{x}\) (c) \(\overline{x}\) – (a – b) (d) \(\overline{x}\) + (a – b)

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