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Here are the annual numbers of deaths from tornadoes in the United States from 1990 through 2000 . (Source: NOAA) 5339336939671309440 A) What is the mean of this data? Round to the hundredths place (2 decimal places). type your answer_ B) What is the standard deviation of this data? Round to the hundredths place (2 decimal places). type your answer_

Ask by Zimmerman Burns. in the United States
Feb 26,2025

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Answer

A) The mean of the data is approximately 591.43. B) The standard deviation of the data is approximately 979.01.

Solution

To find the mean and standard deviation of the given data, we first need to calculate the mean and then the standard deviation. Given data: 533, 933, 693, 967, 130, 944, 0 A) To find the mean: 1. Calculate the sum of all the numbers: Sum = 533 + 933 + 693 + 967 + 130 + 944 + 0 = 4140 2. Calculate the mean by dividing the sum by the total number of data points: Mean = Sum / Total number of data points = 4140 / 7 B) To find the standard deviation: 1. Calculate the variance: Variance = Σ (x - mean)^2 / (n - 1) 2. Calculate the standard deviation: Standard Deviation = √Variance Let's calculate the mean and standard deviation step by step. Calculate the value by following steps: - step0: Calculate: \(\frac{4140}{7}\) The mean of the given data is approximately 591.43. Now, let's calculate the standard deviation. Calculate the value by following steps: - step0: Calculate: \(\left(533-591.43\right)^{2}+\left(933-591.43\right)^{2}+\left(693-591.43\right)^{2}+\left(967-591.43\right)^{2}+\left(130-591.43\right)^{2}+\left(944-591.43\right)^{2}+\left(0-591.43\right)^{2}\) - step1: Subtract the numbers: \(\left(-58.43\right)^{2}+\left(933-591.43\right)^{2}+\left(693-591.43\right)^{2}+\left(967-591.43\right)^{2}+\left(130-591.43\right)^{2}+\left(944-591.43\right)^{2}+\left(0-591.43\right)^{2}\) - step2: Subtract the numbers: \(\left(-58.43\right)^{2}+341.57^{2}+\left(693-591.43\right)^{2}+\left(967-591.43\right)^{2}+\left(130-591.43\right)^{2}+\left(944-591.43\right)^{2}+\left(0-591.43\right)^{2}\) - step3: Subtract the numbers: \(\left(-58.43\right)^{2}+341.57^{2}+101.57^{2}+\left(967-591.43\right)^{2}+\left(130-591.43\right)^{2}+\left(944-591.43\right)^{2}+\left(0-591.43\right)^{2}\) - step4: Subtract the numbers: \(\left(-58.43\right)^{2}+341.57^{2}+101.57^{2}+375.57^{2}+\left(130-591.43\right)^{2}+\left(944-591.43\right)^{2}+\left(0-591.43\right)^{2}\) - step5: Subtract the numbers: \(\left(-58.43\right)^{2}+341.57^{2}+101.57^{2}+375.57^{2}+\left(-461.43\right)^{2}+\left(944-591.43\right)^{2}+\left(0-591.43\right)^{2}\) - step6: Subtract the numbers: \(\left(-58.43\right)^{2}+341.57^{2}+101.57^{2}+375.57^{2}+\left(-461.43\right)^{2}+352.57^{2}+\left(0-591.43\right)^{2}\) - step7: Remove 0: \(\left(-58.43\right)^{2}+341.57^{2}+101.57^{2}+375.57^{2}+\left(-461.43\right)^{2}+352.57^{2}+\left(-591.43\right)^{2}\) - step8: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+341.57^{2}+101.57^{2}+375.57^{2}+\left(-461.43\right)^{2}+352.57^{2}+\left(-591.43\right)^{2}\) - step9: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+\left(\frac{34157}{100}\right)^{2}+101.57^{2}+375.57^{2}+\left(-461.43\right)^{2}+352.57^{2}+\left(-591.43\right)^{2}\) - step10: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+\left(\frac{34157}{100}\right)^{2}+\left(\frac{10157}{100}\right)^{2}+375.57^{2}+\left(-461.43\right)^{2}+352.57^{2}+\left(-591.43\right)^{2}\) - step11: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+\left(\frac{34157}{100}\right)^{2}+\left(\frac{10157}{100}\right)^{2}+\left(\frac{37557}{100}\right)^{2}+\left(-461.43\right)^{2}+352.57^{2}+\left(-591.43\right)^{2}\) - step12: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+\left(\frac{34157}{100}\right)^{2}+\left(\frac{10157}{100}\right)^{2}+\left(\frac{37557}{100}\right)^{2}+\left(-\frac{46143}{100}\right)^{2}+352.57^{2}+\left(-591.43\right)^{2}\) - step13: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+\left(\frac{34157}{100}\right)^{2}+\left(\frac{10157}{100}\right)^{2}+\left(\frac{37557}{100}\right)^{2}+\left(-\frac{46143}{100}\right)^{2}+\left(\frac{35257}{100}\right)^{2}+\left(-591.43\right)^{2}\) - step14: Convert the expressions: \(\left(-\frac{5843}{100}\right)^{2}+\left(\frac{34157}{100}\right)^{2}+\left(\frac{10157}{100}\right)^{2}+\left(\frac{37557}{100}\right)^{2}+\left(-\frac{46143}{100}\right)^{2}+\left(\frac{35257}{100}\right)^{2}+\left(-\frac{59143}{100}\right)^{2}\) - step15: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\left(\frac{34157}{100}\right)^{2}+\left(\frac{10157}{100}\right)^{2}+\left(\frac{37557}{100}\right)^{2}+\left(-\frac{46143}{100}\right)^{2}+\left(\frac{35257}{100}\right)^{2}+\left(-\frac{59143}{100}\right)^{2}\) - step16: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\frac{34157^{2}}{100^{2}}+\left(\frac{10157}{100}\right)^{2}+\left(\frac{37557}{100}\right)^{2}+\left(-\frac{46143}{100}\right)^{2}+\left(\frac{35257}{100}\right)^{2}+\left(-\frac{59143}{100}\right)^{2}\) - step17: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\frac{34157^{2}}{100^{2}}+\frac{10157^{2}}{100^{2}}+\left(\frac{37557}{100}\right)^{2}+\left(-\frac{46143}{100}\right)^{2}+\left(\frac{35257}{100}\right)^{2}+\left(-\frac{59143}{100}\right)^{2}\) - step18: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\frac{34157^{2}}{100^{2}}+\frac{10157^{2}}{100^{2}}+\frac{37557^{2}}{100^{2}}+\left(-\frac{46143}{100}\right)^{2}+\left(\frac{35257}{100}\right)^{2}+\left(-\frac{59143}{100}\right)^{2}\) - step19: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\frac{34157^{2}}{100^{2}}+\frac{10157^{2}}{100^{2}}+\frac{37557^{2}}{100^{2}}+\frac{46143^{2}}{100^{2}}+\left(\frac{35257}{100}\right)^{2}+\left(-\frac{59143}{100}\right)^{2}\) - step20: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\frac{34157^{2}}{100^{2}}+\frac{10157^{2}}{100^{2}}+\frac{37557^{2}}{100^{2}}+\frac{46143^{2}}{100^{2}}+\frac{35257^{2}}{100^{2}}+\left(-\frac{59143}{100}\right)^{2}\) - step21: Rewrite the expression: \(\frac{5843^{2}}{100^{2}}+\frac{34157^{2}}{100^{2}}+\frac{10157^{2}}{100^{2}}+\frac{37557^{2}}{100^{2}}+\frac{46143^{2}}{100^{2}}+\frac{35257^{2}}{100^{2}}+\frac{59143^{2}}{100^{2}}\) - step22: Transform the expression: \(\frac{5843^{2}+34157^{2}+10157^{2}+37557^{2}+46143^{2}+35257^{2}+59143^{2}}{100^{2}}\) - step23: Evaluate the power: \(\frac{5843^{2}+34157^{2}+10157^{2}+37557^{2}+46143^{2}+35257^{2}+59143^{2}}{10000}\) Calculate or simplify the expression \( \sqrt{958466.1143} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{958466.1143}\) - step1: Rewrite the expression: \(\sqrt{\frac{9584661143}{10000}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{9584661143}}{\sqrt{10000}}\) - step3: Simplify the expression: \(\frac{\sqrt{9584661143}}{100}\) The standard deviation of the given data is approximately 979.01. Therefore, the mean of the data is approximately 591.43, and the standard deviation is approximately 979.01.

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To find the mean of the data, add all the annual deaths and divide by the number of years. The total deaths from 1990 to 2000 are 3,771, and there are 11 data points. Dividing gives a mean of approximately 343.73 deaths per year. For the standard deviation, use the formula for standard deviation, which considers the mean, the difference from each number to the mean, and the square of those differences. The calculation results in a standard deviation of approximately 144.87 deaths, indicating the variability in annual deaths due to tornadoes over that decade.

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