Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Consider the following set of ungrouped sample data. Answer parts A through D. 4 4 4 4 12 2 67 80 (A) Find the mean and standard deviation of the ungrouped sample data. x= (Type an integer or a decimal.) S= (Type an integer or decimal rounded to three decimal places as needed.) (B) What proportion of the measurements lies within 1 standard deviation of the mean? Within 2 standard deviations? Within 3 standard deviations? % of the data values fall within 1 standard deviation of the mean. % of the data values fall within 2 standard deviations of the mean. % of the data values fall within 3 standard deviations of the mean.
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Transcribed Image Text:Consider the following set of ungrouped sample data. Answer parts A through D. 4 4 4 4 12 2 67 80 (A) Find the mean and standard deviation of the ungrouped sample data. x= (Type an integer or a decimal.) S= (Type an integer or decimal rounded to three decimal places as needed.) (B) What proportion of the measurements lies within 1 standard deviation of the mean? Within 2 standard deviations? Within 3 standard deviations? % of the data values fall within 1 standard deviation of the mean. % of the data values fall within 2 standard deviations of the mean. % of the data values fall within 3 standard deviations of the mean.
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Step 1: Determine the mean & standerd deviation
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Step 2: Determine the % data values fall within the SD of the mean
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What would the histogram look like?

(C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? Explain. O A. Yes, because most of the data values fall near the mean with fewer data values farther from the mean. O B. No, because most of the data values fall between 2 and 3 standard deviations from the mean. O C. Yes, because about the same number of data values fall near the mean as fall farther above and below the mean. O D. No, because most of the data values fall farther than 3 standard deviations from the mean. (D) To confirm your conjecture, construct a histogram with the class interval width 1 starting at 0.5. Which histogram below shows the data? O A. 6- CIL Frequency 0 2 4 6 8 Din Valm Q Q O B. M T ……… -20 2 4 6 8 10 12 Q Q OC. 0 2 Data Valon 6 Q Q O D. 10- 8+ 6- 0- 0 -N 2 4 Dats Valus || Q 3-
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Transcribed Image Text:(C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? Explain. O A. Yes, because most of the data values fall near the mean with fewer data values farther from the mean. O B. No, because most of the data values fall between 2 and 3 standard deviations from the mean. O C. Yes, because about the same number of data values fall near the mean as fall farther above and below the mean. O D. No, because most of the data values fall farther than 3 standard deviations from the mean. (D) To confirm your conjecture, construct a histogram with the class interval width 1 starting at 0.5. Which histogram below shows the data? O A. 6- CIL Frequency 0 2 4 6 8 Din Valm Q Q O B. M T ……… -20 2 4 6 8 10 12 Q Q OC. 0 2 Data Valon 6 Q Q O D. 10- 8+ 6- 0- 0 -N 2 4 Dats Valus || Q 3-
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Follow-up Questions
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Follow-up Question

What would the histogram look like?

(C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? Explain. O A. Yes, because most of the data values fall near the mean with fewer data values farther from the mean. O B. No, because most of the data values fall between 2 and 3 standard deviations from the mean. O C. Yes, because about the same number of data values fall near the mean as fall farther above and below the mean. O D. No, because most of the data values fall farther than 3 standard deviations from the mean. (D) To confirm your conjecture, construct a histogram with the class interval width 1 starting at 0.5. Which histogram below shows the data? O A. 6- CIL Frequency 0 2 4 6 8 Din Valm Q Q O B. M T ……… -20 2 4 6 8 10 12 Q Q OC. 0 2 Data Valon 6 Q Q O D. 10- 8+ 6- 0- 0 -N 2 4 Dats Valus || Q 3-
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Transcribed Image Text:(C) Based on your answers to part (B), would you conjecture that the histogram is approximately bell shaped? Explain. O A. Yes, because most of the data values fall near the mean with fewer data values farther from the mean. O B. No, because most of the data values fall between 2 and 3 standard deviations from the mean. O C. Yes, because about the same number of data values fall near the mean as fall farther above and below the mean. O D. No, because most of the data values fall farther than 3 standard deviations from the mean. (D) To confirm your conjecture, construct a histogram with the class interval width 1 starting at 0.5. Which histogram below shows the data? O A. 6- CIL Frequency 0 2 4 6 8 Din Valm Q Q O B. M T ……… -20 2 4 6 8 10 12 Q Q OC. 0 2 Data Valon 6 Q Q O D. 10- 8+ 6- 0- 0 -N 2 4 Dats Valus || Q 3-
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