Calculate the Pearson's index of skewness. (Round the mean, median and standard deviation to one decimal place and Pearson's index to two decimal places.) It can be concluded that the distribution is \begin{tabular}{l} (Choose one) \\ significantly \\ not significantly \\ \hline\end{tabular}

To calculate the Pearson's index of skewness, we need to follow these steps: 1. Calculate the mean of the data. 2. Calculate the median of the data. 3. Calculate the standard deviation of the data. 4. Calculate the Pearson's index of skewness using the formula: \[ \text{Pearson's Index of Skewness} = \frac{\text{Mean} - \text{Median}}{\text{Standard Deviation}} \] Let's assume the data is: 1, 2, 3, 4, 5 1. Calculate the mean: \[ \text{Mean} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3 \] 2. Calculate the median: Since the data is already sorted, the median is the middle value, which is 3. 3. Calculate the standard deviation: \[ \text{Standard Deviation} = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \text{Mean})^2}{n}} \] \[ \text{Standard Deviation} = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5}} \] \[ \text{Standard Deviation} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} \] \[ \text{Standard Deviation} = \sqrt{\frac{10}{5}} \] \[ \text{Standard Deviation} = \sqrt{2} \] 4. Calculate the Pearson's index of skewness: \[ \text{Pearson's Index of Skewness} = \frac{3 - 3}{\sqrt{2}} = 0 \] Since the Pearson's index of skewness is 0, it indicates that the distribution is not significantly skewed. Therefore, the distribution is not significantly skewed.