AP Physics                                                                               Brockport High School NY USA
Science and Statistics                                                              Mr Keefer

Introduction
        Statistics is the mathematics of collecting and analyzing data.  Statistical analysis allows scientists, engineers, psychologists, and other researchers to analyze and interpret their data objectively and therefore determine the reliability of the data collected.  This allows a researcher to decide if an experiment should be repeated or changed, or if a whole new approach should be taken with modifications to a theory.  Statistics also allows for the analysis of reliability in industrial equipment.

Statistical Terms
mean - the average of all data collected.
median - the middle measurement in a set of data.
mode - the most frequently occurring measurement.
range - the difference between the highest and lowest measurement.
dispersion - a measure of "clustering@ of data points around the center.

Determining dispersion
1.  Mean deviation is the average deviation from the mean.  It is a weak indicator of dispersion and is seldom used in statistics.  It can be used to compare dispersion in two or more experiments.                       
2.  Variance is the average sum of the squares of the deviations from the mean.  It is designated by the lower case Greek letter sigma, s2, and is used to calculate the more popular statistic called standard deviation.  To find s2, sum the squares of the deviations from the mean and divide by the total number of observations minus 1 (this procedure adjusts for bias and is called the degrees of freedom).
3.  Standard Deviation (s) is a measure of dispersion about the mean that allows us to predict what percentage of data points should be expected at various deviations from the mean.  To find standard deviation, take the square root of the variance.  The typical dispersion pattern can be assumed as:

            68% of measurements fall within "1 s of the mean
95% fall within "2 s of the mean
99.73% fall within "3 s of the mean

Example:

The following are heights (in meters) of 11 students at Brockport High School:

1.70      1.85      1.65      1.60      1.35      1.55      1.60      1.40      1.80      1.75      1.60

Find the mean.            _________m
Find the range.           _________m
Find the median.        _________m
What is the mode?     _________m
Calculate the variance (s2).   [(1.70 - mean)2 + (1.85 - mean)2 + ...] / (11 -1)
Calculate the standard deviation (s) by taking the square root of the variance.
Determine the range of heights that will include 68% of all seniors, and 95% of all seniors. 

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