ex2 - EXPERIMENT 2 Reaction Time Objectives to make a...

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1 EXPERIMENT 2 Reaction Time Objectives to make a series of measurements of your reaction time to make a histogram, or distribution curve, of your measured reaction times to calculate the "average" or mean of these reaction measurements as a "best value" to calculate the "standard deviation" or “uncertainty” associated with an individual measurement to calculate the "standard deviation" associated with the mean value to compare your calculations with the data displayed on the histogram, and with the prediction from the "normal" or Gaussian distribution to discuss the significance of data comparison when the spread in values is large Theory Two of the main purposes of this experiment are to familiarize you with the taking of experimental data and with the reduction of such data into a useful and quantitative form. In any experiment, one is concerned with the measurement of some physical quantity. In this particular experiment it will be your reaction time. When you make repeated measurements of a quantity you will find that your measurements are not all the same, but vary over some range of values. As the spread of the measurements increases, the reliability or precision of the measured quantity becomes poorer. If the measured quantity is to be of any use in further work, or to other people, it must be capable of being described in simple terms. One method of picturing measured values of a single quantity is to create a histogram. The histogram is a diagram drawn by dividing the original set of measurements into intervals or “bins” of predetermined size, and counting the number of measurements within each bin. One then plots the frequency (the number of times each value occurs) versus the values themselves. The histogram has the advantage of visually presenting the distribution of readings or measurements. Figure 1 shows a typical histogram for a set of observations. When placing the values into bins, one systematically puts values that occur on the bin limits into the next higher bin.
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2 Figure 1 Typical histogram (bin size = 10) When analyzing data with a histogram, the distribution often times suggests that there is a "best" or most likely value, around which the individual measurements are grouped. From an intuitive approach one might say that the best value is somehow related to the middle of the distribution, while the uncertainty is related to the spread of the distribution. The following formulas, which we will define, will in general only have significance for symmetrical distributions. Using mathematical statistical theory it turns out that the best value is nothing more than the arithmetic average or mean of our measurements, which we will denote with the symbol: x .
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This note was uploaded on 07/25/2008 for the course PHY 251 taught by Professor J.t. during the Summer '08 term at Michigan State University.

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ex2 - EXPERIMENT 2 Reaction Time Objectives to make a...

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