Multiple choice

A distribution consists of three components with frequencies $45, 40$ and $15$ having their means $2, 2.5, 2$ respectively. The mean of the combined distribution is

  1. $2.1$
  2. $2.2$
  3. $2.3$
  4. $2.4$
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B Correct answer
Explanation

Combined mean = (f1*m1 + f2*m2 + f3*m3) / (f1 + f2 + f3) = (45*2 + 40*2.5 + 15*2) / (45+40+15) = (90 + 100 + 30) / 100 = 220 / 100 = 2.2.

AI explanation

Use the combined mean formula: (f1m1 + f2m2 + f3m3) / (f1 + f2 + f3). The numerator is (45 * 2) + (40 * 2.5) + (15 * 2) = 90 + 100 + 30 = 220. The denominator is 45 + 40 + 15 = 100. Dividing 220 by 100 gives a mean of 2.2.

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