Part 3 of 5 Calculate the Pearson's index of skewness. (Round the mean, median and standard deviation to one decimal place and Pearson's index to two decir places.) \[ \mathrm{PI}=\square \] It can be concluded that the distribution is not significantly \( \mathbf{\nabla} \) skewed. \( \square \) Try one last time Skip Part Recheck Save For Later © 2025 McGraw Hill LLC. All Riahts Resenved. Terms of Use I

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: \[ \mathrm{PI} = \frac{\mathrm{Mean} - \mathrm{Median}}{\mathrm{Standard Deviation}} \] Let's assume we have a dataset: \( \{1, 2, 3, 4, 5\} \) 1. Calculate the mean: \[ \mathrm{Mean} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3 \] 2. Calculate the median: Since the dataset is already sorted, the median is the middle value, which is 3. 3. Calculate the standard deviation: \[ \mathrm{Standard Deviation} = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \mathrm{Mean})^2}{n}} \] \[ \mathrm{Standard Deviation} = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5}} \] \[ \mathrm{Standard Deviation} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} \] \[ \mathrm{Standard Deviation} = \sqrt{\frac{10}{5}} \] \[ \mathrm{Standard Deviation} = \sqrt{2} \] 4. Calculate the Pearson's index of skewness: \[ \mathrm{PI} = \frac{3 - 3}{\sqrt{2}} = 0 \] Therefore, the Pearson's index of skewness is 0, indicating that the distribution is not significantly skewed.