36 Three stodents named Abe, Barb, and Cal make measurements (in m) of the length of...

 

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36 Three stodents named Abe, Barb, and Cal make measurements (in m) of the length of a table using a meter stick. Each student's measurements are tabulated in the table below along with the mean, the standard deviation from the mean, and the standard error of the measurements Shudent La 柔 Abe 1.4717 1.4711 14722 1.4715 1.4716 0.00046 0.0002 Barb 1.4753 1.4759 1.4756 1.4749 1.4754 0.00043 0.0002 Cal 1.4719 1.4723 1.4727 1.4705 1.4719 0.00096 0.0005 Note that in each case only one significant figure is kept in the standard error a, and this determines the number of significant figures in the mean. The actual length of the table is determined by very sophisticated laser measurement techniques to be 1.4715 m. 18 ynies Lahorutery Munal Layd 3. State how one determines the accuracy of a measurement. Apply your idea to the measurements of the three students above and state which of the stuadents has the most accurate measurement. Why is that youar conclusion? 4. Apply Equations 1, 2, and 3 to calculate the mean, standard deviation, and standard error for Abe's measurements of length. Confirm that your calculated values are the same as those in the table. Show your calculations explicitly. 5. State the characteristics of data that indicate a systematic error. Do any of the three shadents have data that suggest the possibility of a systematic error? If so, state which student it is, and state how the data indicate your conclusion. 6. Which student has the best measurement considering both accuracy and precision? State clearly what the characteristics are of the student's data on which your answer is based. 36 Three stodents named Abe, Barb, and Cal make measurements (in m) of the length of a table using a meter stick. Each student's measurements are tabulated in the table below along with the mean, the standard deviation from the mean, and the standard error of the measurements Shudent La 柔 Abe 1.4717 1.4711 14722 1.4715 1.4716 0.00046 0.0002 Barb 1.4753 1.4759 1.4756 1.4749 1.4754 0.00043 0.0002 Cal 1.4719 1.4723 1.4727 1.4705 1.4719 0.00096 0.0005 Note that in each case only one significant figure is kept in the standard error a, and this determines the number of significant figures in the mean. The actual length of the table is determined by very sophisticated laser measurement techniques to be 1.4715 m. 18 ynies Lahorutery Munal Layd 3. State how one determines the accuracy of a measurement. Apply your idea to the measurements of the three students above and state which of the stuadents has the most accurate measurement. Why is that youar conclusion? 4. Apply Equations 1, 2, and 3 to calculate the mean, standard deviation, and standard error for Abe's measurements of length. Confirm that your calculated values are the same as those in the table. Show your calculations explicitly. 5. State the characteristics of data that indicate a systematic error. Do any of the three shadents have data that suggest the possibility of a systematic error? If so, state which student it is, and state how the data indicate your conclusion. 6. Which student has the best measurement considering both accuracy and precision? State clearly what the characteristics are of the student's data on which your answer is based.

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