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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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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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 Summer '08
 J.T.
 Physics, Normal Distribution, Standard Deviation, Mean

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