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# The weights of ten young turkeys to the nearest 0.1 kg are: 0.8, 1.1, 1.2, 0.9, 1.2, 1.2, 0.9, 0.7, 1.0, 1.1 a. Find the mean and standard deviation for the turkeys. b. After being fed a special diet for one month, the weights of the turkeys doubled. Find the new mean and standard deviation. c. Comment, in general terms, on your findings from a and b.

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$\textbf{(a)}$ We know that the formula for mean $\bar{x}$ with score value $x_i$ and total items $n$ is,

$\bar{x}=\dfrac{\sum x_i}{n}$

This implies that the mean value for the given weight data would be,

\begin{align*} \bar{x} &= \dfrac{0.8+1.1+1.2+0.9+1.2+1.2+0.9+0.7+1.0+1.1}{10}\\\\ \bar{x} &= \dfrac{10.1}{10}\\\\ \bar{x} &= 1.01\\ \end{align*}

Next, there are two ways to calculate the standard deviation.

Case 1: If we consider the given sample as whole population then the formula for the standard deviation $s$ with score value $x_i$ and mean $\bar{x}$ is,

$s=\sqrt{\dfrac{\sum (x_i - \bar{x})^2}{n}}$

Case 2: When we use the sample as an estimate of the whole population then the formula for the standard deviation $s$ with score value $x_i$ and mean $\bar{x}$ is,

$s=\sqrt{\dfrac{\sum (x_i - \bar{x})^2}{n - 1}}$

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