The mean of a set of numbers is bar x. If lam | vedclass

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(D) Let the set of $n$ numbers be $x_1, x_2, ..., x_n$. The mean is given by $\bar x = \frac{1}{n} \sum_{i=1}^{n} x_i$. If $\lambda$ is subtracted fro

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$\bar x - \lambda$

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(D) Let the set of $n$ numbers be $x_1, x_2, ..., x_n$. The mean is given by $\bar x = \frac{1}{n} \sum_{i=1}^{n} x_i$. If $\lambda$ is subtracted from each number,the new set becomes $(x_1 - \lambda), (x_2 - \lambda), ..., (x_n - \lambda)$. The new mean $\bar x_{new}$ is $\frac{1}{n} \sum_{i=1}^{n} (x_i - \lambda)$. This simplifies to $\frac{1}{n} (\sum_{i=1}^{n} x_i - \sum_{i=1}^{n} \lambda) = \frac{1}{n} (\sum_{i=1}^{n} x_i - n\lambda)$. Thus,$\bar x_{new} = \frac{1}{n} \sum_{i=1}^{n} x_i - \frac{n\lambda}{n} = \bar x - \lambda$.

The mean of a set of numbers is $\bar x$. If $\lambda$ is subtracted from each number,what will be the mean of the new set?

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