Any measured value has some uncertainty. Causes for the uncertainty can be
measurement noise, outcomes due to effects other than the one we are
measuring^{1}, or even the possibility that the measurement was just made
incorrectly (possible equipment malfunctions).

We will use some basic **statistical analyses** in this section to examine
measurement variations. Statistics are a way to quantify variations in results
which are due to random effects—or minimize the significance of these
effects on our final conclusions. Some basic information relative to common
statistical quantities used to characterize data is provided in the Basic
Statistics link of this experiment.

Microsoft^{®} Excel™ and MATLAB^{®} are software
packages which are commonly used by engineers to perform calculations. Both
software packages have built-in capabilities for performing statistics. Some
Microsoft Excel and MATLAB commands which can be used to perform the analyses
necessary in this exercise are provided at the links to the right.

This exercise uses concepts introduced in our experiment on Ohm's law. A link to this experiment is provided in the related materials section as well.

Pick any resistor from your parts kit—as long as the third band on the color code is orange. From the color code on the resistors, determine the expected (nominal) resistance of the resistors. Record this value.

Use your DMM as an ohmmeter to measure the resistances of the resistor. Record this value.

Use your Analog Discovery™ and DMM to apply a range of voltages to your resistor and measure the resulting currents.

Use the

**mA**setting on the DMM.Apply voltages of 0V, 1V, 2V, 3V, and 4V to the resistor (you will need to use the waveform generator on the Analog Discovery to apply these voltages). Record the measured currents corresponding to these voltages. Calculate the resistance for each combination of voltage and current.

Calculate the mean and standard deviation of these resistance values.

Repeat Step 3, but use the **µA** setting on your DMM.

Compare the mean and standard deviation values you calculated in Steps 3 and 4. Which mean value do you think best reflects the actual resistance of the resistor? Why?

Also compare the mean resistance with the nominal resistance (determined from the resistor color codes in Step 1) and the resistance measured with the DMM. Are the measured resistances from Steps 3, 4, and 5 all within the manufacturer's tolerances? Which resistance value do you think is most accurate? Why

^{2}?

^{1}For example, resistance can be a function of temperature. If we measure the resistance of a resistor while its temperature varies, we can get measured resistance variations which have nothing to do with the material properties of the resistor itself.^{2}Please don't immediately claim that the DMM is the most accurate (although it probably is) without trying to find out something about how the DMM works. Your owner's manual can help with this, as can a quick internet search.

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