2.8 Inductive Process: 1. Data & their Uncertainties: An inclined-plane experiment was carried out in order to reconstruct Galileo's experiment. One of the data sets with 6 feet plane and inclination angle of 4.47 degrees is shown below: At (Ax=d/4) At (Ax=d/2) At (Ax=3/4) At (Ax=d) [s] [s] Trial #1 1.20 1.800 2.30 Trial #2 1.30 2.001 2.40 Trial #3 1.30 1.80 2.30 Trial #4 1.30 1.80 2.30 Trial #5 1.200 1.90 At (average) 1.26 1.86 2.30 At (s.d.) 0.06 0.09 0.05 Random Error of At 0.02 0.04 2.30 0.02 Q1: Why do we need to measure the same quantity At five times? In each column there are five measurements and their average, which quantity is the most precise measurement of At? Q2: What is the definition of standard deviation (s.d.) of each set of five measurements? Which characteristics (center, spread, skewness,...etc. of data) of each set of five measurements does it represent? Q3: What is the definition of random error for each averaged At? What does it represent? Why its value is smaller than that of the corresponding standard deviation? 2.8 Inductive Process: 1. Data & their Uncertainties: An inclined-plane experiment was carried out in order to reconstruct Galileo's experiment. One of the data sets with 6 feet plane and inclination angle of 4.47 degrees is shown below: At (Ax=d/4) At (Ax=d/2) At (Ax=3/4) At (Ax=d) [s] [s] Trial #1 1.20 1.800 2.30 Trial #2 1.30 2.001 2.40 Trial #3 1.30 1.80 2.30 Trial #4 1.30 1.80 2.30 Trial #5 1.200 1.90 At (average) 1.26 1.86 2.30 At (s.d.) 0.06 0.09 0.05 Random Error of At 0.02 0.04 2.30 0.02 Q1: Why do we need to measure the same quantity At five times? In each column there are five measurements and their average, which quantity is the most precise measurement of At? Q2: What is the definition of standard deviation (s.d.) of each set of five measurements? Which characteristics (center, spread, skewness,...etc. of data) of each set of five measurements does it represent? Q3: What is the definition of random error for each averaged At? What does it represent? Why its value is smaller than that of the corresponding standard deviation