Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable $x$ represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births. Table of numbers of girls and probabilities \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Number of \\ Girls $\mathbf{x}$ \end{tabular} & $\mathbf{P}(\mathbf{x})$ \\ \hline 0 & 0.004 \\ 1 & 0.034 \\ 2 & 0.103 \\ 3 & 0.224 \\ 4 & 0.259 \\ 5 & 0.227 \\ 6 & 0.119 \\ 7 & 0.026 \\ 8 & 0.004 \\ \hline \end{tabular}

Step 1 ：We are given a table that describes the results from groups of 8 births from 8 different sets of parents. The random variable $x$ represents the number of girls among 8 children. We are asked to find the mean and standard deviation for the number of girls in 8 births.

Step 2 ：The mean and standard deviation of a probability distribution can be calculated using the formulas: Mean ($\mu$) = $\sum [x * P(x)]$ and Standard Deviation ($\sigma$) = $\sqrt{\sum [(x - \mu)^2 * P(x)]}$

Step 3 ：Let's denote the number of girls as $x$ and their corresponding probabilities as $P_x$. So, $x = [0, 1, 2, 3, 4, 5, 6, 7, 8]$ and $P_x = [0.004, 0.034, 0.103, 0.224, 0.259, 0.227, 0.119, 0.026, 0.004]$

Step 4 ：Using the formula for the mean, we calculate $\mu = \sum [x * P(x)] = 4.011$

Step 5 ：Using the formula for the standard deviation, we calculate $\sigma = \sqrt{\sum [(x - \mu)^2 * P(x)]} = 1.416$

Step 6 ：Final Answer: The mean number of girls in 8 births is \(\boxed{4.011}\) and the standard deviation is \(\boxed{1.416}\)