Multiple choice

The mean of a set of observation is $a$. If each observation is multiplied by $b$ and each product is decreased by $c$ then the mean of new set of observation is

  1. $\displaystyle \frac{a}{b}+c $
  2. $ab - c$
  3. $\displaystyle \frac{a}{b}-c $
  4. $ab + c$
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B Correct answer
Explanation

If each observation x is transformed to (b * x - c), the new mean is b * (old mean) - c. Given the old mean is a, the new mean is ab - c.

AI explanation

Using the algebraic properties of the arithmetic mean, when every observation is multiplied by a constant b, the new mean is also multiplied by b, resulting in a times b. Furthermore, when a constant c is subtracted from every observation, that same constant is subtracted from the mean. Therefore, the final mean of the new set of observations is a times b minus c.

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