Questions Related to average

Multiple choice maths average arithmetic mean of ap introduction to averages means

The average weight of 45 students in a class is 25 kg. Five of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?

  1. $52\frac{1}{3}$
  2. $52\frac{1}{2}$
  3. $52\frac{2}{3}$
  4. None of these

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Multiple choice maths average arithmetic mean of ap introduction to averages means

A line is such that the algebraic sum of the perpendicular on it from a number of point is zero. The line always passes through a fixed point that is 

  1. A. M of the given points

  2. GM of the given points

  3. HM of the given points

  4. None of these

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Explanation

The algebraic sum of perpendiculars from points (xi, yi) to a line ax + by + c = 0 being zero implies the line passes through the centroid (mean of x, mean of y).

Multiple choice maths average arithmetic mean of ap introduction to averages means

If the arithmetic mean of the numbers $x _{1}, x _{2}, x _{3}.......,x _{3}$ is $\overline{X}$, then the arithmetic mean of numbers $ax _{1}+b, ax _{2}+b, ax _{3}+b,........, ax _{n}+b$, where  $a, b$ are two constants would be 

  1. $\overline{X}$
  2. $na\overline{X}+nb$
  3. $a\overline{X}$
  4. $a\overline{X}+b$
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