Lab_2_210

MSE 210 Engineering Measurement and Data Analysis 1/4 Lab 2: Engineering Measurement Name: Student number:_ Name:__ Student number Objectives In this lab, you will collect and analyze some data with a random nature with the goal of familiarizing yourself with the concept of variability. You will also need to graphically present the collected data and propose a proper distribution function for it. In the last part of the lab, you will study error propagation in experiments. 1. Data collection You will be provided with 25 capacitors with a nominal value of 10nF. Using your digital multimeter, measure the capacitance of each of these capacitors and record your observations in the table below (denoted C 1 ). Report 3 significant digits for your measurements (make sure that you are using the multimeter correctly). C 1 Capacitance (nF) C 1 Capacitance (nF) C 1 Capacitance (nF) C 1 Capacitance (nF) 1 8 15 22 2 9 16 23 3 10 17 24 4 11 18 25 5 12 19 6 13 20 7 14 21 What are the mean and standard deviation of the measured capacitances? μ C1 = _____________ σ C1 = _____________ 2. Graphical presentation 2.a. Histogram of the data Draw the histogram for the frequency of the capacitance values. How do you choose the number of

MSE 210 Engineering Measurement and Data Analysis 2/4 bins?

MSE 210 Engineering Measurement and Data Analysis 4/4

MSE 210 Engineering Measurement and Data Analysis 5/4 3. Rejection of data Identify a data point in collected values for C 1 that you might consider suspicious. Use the Chauvenet`s criterion to decide whether you should reject this point from your data or not (assume the data has a normal distribution). 4. Fitting to a distribution Using the “probplot” function in Matlab (attach Matlab plots to your report), find out which one of these distributions describes the data better: normal, lognormal, weibull? Distribution of data: _________weibull___________ How would you make a decision in this case if the plots for normal and lognormal distributions do not produce a clear distinction? Answer: USE THE KOLMOGOROV – SMIRNOV TEST OR ANDERSON – DARLING TEST

MSE 210 Engineering Measurement and Data Analysis 7/4 5. Propagation of errors Get ten 100nF capacitors (denoted C 2 ) from the TAs and do the same measurements as in step 1 to find the mean and standard deviation of the measured capacitances. C 2 1 2 3 4 5 6 7 8 9 10 capacitance μ C2 = _____101.59________ σ C2 = ________3.4565_____ Pair up the 100nF capacitors with another ten 10nF capacitors from your original batch. Using the breadboard, place each pair in parallel and record the equivalent capacitance (denotes Cp). C p 1 2 3 4 5 6 7 8 9 10 capacitance What are the values of mean and standard deviation for the combination of the

MSE 210 Engineering Measurement and Data Analysis 8/4 capacitors? μ Cp = ___110.22________ σ Cp = ___2.7174_________ How do these numbers compare with the theoretical values? Hint: Report uncertainties in the normal distribution based on 95% significance level (uncertainty, δ= 2 σ) For parallel connection of capacitors, C p = C 1 + C 2 Explain your choice of error propagation approach. Answer: The values closely align with the anticipated 110 uF expected value, with each measurement falling within the 95% significance level. Employing a 2σ uncertainty approach proves pragmatic, as it ensures a conservative estimation of uncertainty. This method acknowledges the possibility of a greater actual uncertainty than the standard deviation σ, particularly in situations where measurements may be influenced by undisclosed or uncontrollable factors.