Question
What is the significance of standard deviation in the analysis of the data of an analytical determination? The result (R) of an analytical determination depends on three parameters as per the relation, R= (A+B)/C. The values and individual absolute standard deviations (given in parentheses) of the three quantities, A, B and C obtained in an experimental determination are given below. Calculate the standard deviation in the result, R of the determination. A = 3.80 (± 0.04), B = 2.10 (±0.02), C = 1.97 (±0.03)
Answer :
Word Count : 295
To calculate the standard deviation of the result \( R \) based on the given formula \( R = \frac{A + B}{C} \), we use the propagation of uncertainty method. When performing calculations involving multiple variables, the standard deviation of the result can be calculated by: \[ \left( \frac{\sigma_R}{R} \right)^2 = \left( \frac{\sigma_A}{A} \right)^2 + \left( \frac{\sigma_B}{B} \right)^2 + ____ _____ __________ ________ ______ ______.
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To calculate the standard deviation of the result \( R \) based on the given formula \( R = \frac{A + B}{C} \), we use the propagation of uncertainty method. When performing calculations involving multiple variables, the standard deviation of the result can be calculated by: \[ \left( \frac{\sigma_R}{R} \right)^2 = \left( \frac{\sigma_A}{A} \right)^2 + \left( \frac{\sigma_B}{B} \right)^2 + ____ _____ __________ ________ ______ ______.
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