Multiple choice

Mean of $n$ observations $x_{1}, x_{2}, ...., x_{n}$ is $\overline {x}$. If an observation $x_{q}$ is replaced by $x_{q}'$ then the new mean is

  1. $\overline {x} - x_{q} + x'_{q}$
  2. $\dfrac {(n - 1)\overline {x} + x'_{q}}{n}$
  3. $\dfrac {(n - 1)\overline {x} - x'_{q}}{n}$
  4. $\dfrac {n\overline {x} - x_{q} + x'_{q}}{n}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of original observations = n * x_bar. New sum = n * x_bar - x_q + x_q'. New mean = (n * x_bar - x_q + x_q') / n.

AI explanation

The original sum of the n observations is n times the mean. When an observation is replaced, the new sum becomes n*x-bar - x_sub_q + x_prime_sub_q. The new mean is found by dividing this updated sum by n, resulting in the formula (n*x-bar - x_sub_q + x_prime_sub_q) / n.

Keep practicing — related questions