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The following set of data is a collection of fall times for a ball dropped from rest of a 20.0 meter building. 2.011 seconds 2.026 seconds 2.033 seconds 2.014 seconds 2.019 seconds 2.020 seconds Find the mean and RMS for these times. Part 4: Measurement and Perception Our eyes and minds can deceive us and produce errors in our measurements and perceptions! Using observation only, answer the questions in the column on the left. Then measure the objects to the nearest tenth of a millimeter. Then answer the questions in column on the right. Can you trust your own eyes? Be honest!! שהיו Folom "Tab3 ESTRd Mensur Distinen ANNA ER AVENTARERT I FRIPLE TOPPER CERTANTORENE when Which open the mom ? Tole Which pole is the talent? which appear DI CIE WABC long Which line is longer meis CES Der DC widow with a winnat Are the Spalle parallel ye Whili KE When til lon KI LM KIM WIR UM le NO TO סדר WHITE come To longer ES ttt represents the best measurement. The arithmetic mean of a set of numbers is simply the sum of the numbers divided by the number of numbers. Thus, the mean of 1, 2, and 3 is (1 +2 + 3) 13 = 6/3 = 2 Now we go one step further with the mean. That is, we determine how far each measurement differs from the average. To do this, we simply subtract the average from each of the measured numbers and call their values the deviations. The deviations for the above example are 1-2=-1 2- 2 = 0 3 - 2 = 1 Now if we disregard the sign of the deviations, we may calculate the average deviation by finding the average of the individual deviations 1,0, and 1: (1 +0+ 1)/3 = 2/3 = 0.667 We can think of the average deviation as the average distance from the mean. For mathematical reasons it turns out that it is better to measure the average deviation from the mean using the root-mean-square measure for average. If{q1, 92, ..., qn} are n measurements of a quantity q, then the average mean deviation, which is known in statistics as the RMS and is denoted by the subscripts qrms, is given by the formula 9mm = N2 (91-(9)) im where (9) = -HE) is the average of the numbers [91,92,... qn). For the values above the RMS becomes {(-1)+02 + 12) = Prm = --- = 0.817 which in this example is more than the average of the absolute values of the deviations given above. In this lab, the average and RMS will be a set of standard tools for analyzing measured data. In some of your experiments you will be working with large data sets. In this case you will be asked to use Microsoft Excel. In Excel, the average function is "AVERAGE" and the RMS is "STDEV.P" which can be found in Statistical Function menu. The average and RMS allow us to replace a large set of data for a measured quantity that were obtained from repeated trials by two mumbers: the average value of the data set and the RMS. For example, the set of repeated measurements: 1, 2, 3 is represented by 2+0.817, i.e., the measurements differ from the average 2 by plus or minus 1. At least now we have a way to state the results of repeated measurements. Keep this technique in mind since you'll be using this when you analyze your experiments. Precision & Accuracy By their nature, measurements can never be done perfectly. Part of the error in making measurements may be due to the skill of the person making the measurement, but even the most skillful among us cannot make the perfect measurement. Basically this is because no matter how small we make the divisions on our ruler (using distance as an example) we can never be sure that the thing we are measuring lines up perfectly with one of the marks. Therefore the judgment of the person doing the measurement plays a significant role in the accuracy and precision of the measurement. High accuracy, Accuracy: Accuracy describes the nearess of a measurement to the standard or true value, i.e., a highly accurate measuring device will provide measurements very close to the standard, true or known values. Example: in target shooting a high score indicates the neamess to the bull's eye and is a measure of the shooter's accuracy. Precision: Precision is the degree to which several measurements provide answers very close to each other. It is an indicator of the scatter in the data. The lesser the scatter, the higher the precision. but low precision Ideally, we want to make measurements that are both accurate AND precise. However, we can never make a perfect measurement. The best we can do is to come as close as possible within the limitations of the measuring instruments. Mich precision, but low aceacy Uncertainty A measurement result in science is meaningless without a Since we can never make a quantitative statement of the uncertanty perfect measurement, every measurement is approximate. Therefore it is important to always report the amount of confidence we have in our measurements, what we call experimental uncertainty. For example, you may estimate the length of the lab bench to be "5 meters give or take a meter". The "give or take part is an expression of your confidence in your estimate. In scientific measurements we say "plus or minus" but it means the same as "give or take." We write that our measurement of the length, represented by "L" is : L=5m +/- 1m If you are using a scale such as a ruler to measure the length of an object, then your uncertainty is usually estimated to be one tenth the smallest division. For example, this bug has a length between 1.54 and 1.56 in or L=1.55in +/-0.Olin The 1.55in is the average measure and the 0.0lin is the uncertainty. Error An experimental error is not a mistake! It is the difference between a measurement and an accepted value of something For example, if you determine from an experiment that the acceleration due to gravity is 10 m/s then the 'error' is the difference between that value and the accepted value of 9.8m's, or 0.2m/s. The error can also be expressed as a percent: 10-9.8 % error = -X100% = 2% 9.8
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Physics

Part 3
Mean = sum/ number of items n
(2.011+2.026+2.033+2.014+2.019+2.020)...


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