WBJEE · Maths · Statistics
Mean of \(n\) observations \(x_{1}, x_{2}, \ldots, x_{n}\) is \(\bar{x}\). If an observation \(x_{q}\), is replaced by \(x_{q}^{\prime}\) then the new mean is
- A \(\bar{x}-x_{q}+x_{q}^{\prime}\)
- B \(\frac{(n-1) \bar{x}+x_{q}^{\prime}}{n}\)
- C \(\frac{(n-1) \bar{x}-x_{q}^{\prime}}{n}\)
- D \(\frac{n x-x_{q}+x_{q}^{\prime}}{n}\)
Answer & Solution
Correct Answer
(D) \(\frac{n x-x_{q}+x_{q}^{\prime}}{n}\)
Step-by-step Solution
Detailed explanation
We have, \[ \bar{x}=\frac{x_{1}+x_{2}+\ldots+x_{q}+\ldots+x_{2}}{n} \] \(\Rightarrow \quad \Sigma x=n \bar{x}\) If \(x_{q}\), is replaced by \(x_{q}^{\prime}\), then new total will be \(\Sigma x'=\Sigma x-x_{4}-x_{4}^{\prime}\) New mean will be…
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