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.
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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