Practice 1: During a thunderslam, Nasaean used a whd speed gauge to measure the whd gusts. The whd gusts, in miles per hour, were \( 19, 24, 10, 15, 21, 35 \), and 16. Identify any outliers in the data set. A. 10 B. 15.5 C. 35 D. None

To identify any outliers in the data set, we need to calculate the mean and standard deviation of the given whd gusts. Given data set: \( 19, 24, 10, 15, 21, 35, 16 \) 1. Calculate the mean of the data set: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}} \] 2. Calculate the standard deviation of the data set: \[ \text{Standard Deviation} = \sqrt{\frac{\text{Sum of squared differences from mean}}{\text{Total number of values} - 1}} \] After calculating the mean and standard deviation, we can identify any outliers by comparing the values with the mean and standard deviation. Let's calculate the mean and standard deviation of the given data set. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(19+24+10+15+21+35+16\right)}{7}\) - step1: Remove the parentheses: \(\frac{19+24+10+15+21+35+16}{7}\) - step2: Add the numbers: \(\frac{140}{7}\) - step3: Reduce the numbers: \(\frac{20}{1}\) - step4: Calculate: \(20\) Calculate or simplify the expression \( \sqrt{\frac{(19-20)^2+(24-20)^2+(10-20)^2+(15-20)^2+(21-20)^2+(35-20)^2+(16-20)^2}{7-1}} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{\left(19-20\right)^{2}+\left(24-20\right)^{2}+\left(10-20\right)^{2}+\left(15-20\right)^{2}+\left(21-20\right)^{2}+\left(35-20\right)^{2}+\left(16-20\right)^{2}}{7-1}}\) - step1: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+\left(24-20\right)^{2}+\left(10-20\right)^{2}+\left(15-20\right)^{2}+\left(21-20\right)^{2}+\left(35-20\right)^{2}+\left(16-20\right)^{2}}{7-1}}\) - step2: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+4^{2}+\left(10-20\right)^{2}+\left(15-20\right)^{2}+\left(21-20\right)^{2}+\left(35-20\right)^{2}+\left(16-20\right)^{2}}{7-1}}\) - step3: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+4^{2}+\left(-10\right)^{2}+\left(15-20\right)^{2}+\left(21-20\right)^{2}+\left(35-20\right)^{2}+\left(16-20\right)^{2}}{7-1}}\) - step4: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+4^{2}+\left(-10\right)^{2}+\left(-5\right)^{2}+\left(21-20\right)^{2}+\left(35-20\right)^{2}+\left(16-20\right)^{2}}{7-1}}\) - step5: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+4^{2}+\left(-10\right)^{2}+\left(-5\right)^{2}+1^{2}+\left(35-20\right)^{2}+\left(16-20\right)^{2}}{7-1}}\) - step6: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+4^{2}+\left(-10\right)^{2}+\left(-5\right)^{2}+1^{2}+15^{2}+\left(16-20\right)^{2}}{7-1}}\) - step7: Subtract the numbers: \(\sqrt{\frac{\left(-1\right)^{2}+4^{2}+\left(-10\right)^{2}+\left(-5\right)^{2}+1^{2}+15^{2}+\left(-4\right)^{2}}{7-1}}\) - step8: Evaluate the power: \(\sqrt{\frac{1+4^{2}+\left(-10\right)^{2}+\left(-5\right)^{2}+1^{2}+15^{2}+\left(-4\right)^{2}}{7-1}}\) - step9: Evaluate the power: \(\sqrt{\frac{1+4^{2}+\left(-10\right)^{2}+\left(-5\right)^{2}+1+15^{2}+\left(-4\right)^{2}}{7-1}}\) - step10: Add the numbers: \(\sqrt{\frac{384}{7-1}}\) - step11: Subtract the numbers: \(\sqrt{\frac{384}{6}}\) - step12: Divide the terms: \(\sqrt{64}\) - step13: Write in exponential form: \(\sqrt{8^{2}}\) - step14: Simplify the root: \(8\) The mean of the given data set is 20 and the standard deviation is 8. Now, let's compare the values in the data set with the mean and standard deviation to identify any outliers. Outliers are values that are significantly higher or lower than the mean. In this case, the value 35 is significantly higher than the mean (20) and is more than 2 standard deviations away from the mean. Therefore, 35 is an outlier in the data set. So, the correct answer is: C. 35