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Section 2.3 2.7
Center
Spread
Calculating median,
m
Arrange the
n
measurements from smallest to largest
1.
If
n
is odd
m
is the middle number
2.
If
n
is even
m
is the mean of the middle two numbers
Skewed data
Median <Mean Rightward skewness
Mean=Median symmetric
Median
Mean
Mean
Median
Mean<Median Leftward skewness
(Rightward)
(Leftward)
Mode Most frequently
Range Largest measurement minus the smallest measurement
Sample variance
or
Sample standard deviation
Standard deviation: The amount of variability in the [time] it takes something to complete
Chebyshevs Rule: Interpreting the standard deviation. Applies to any data set regardless of the shape of the frequency distribution of
the data
No useful information is provided on the fraction of measurements that fall within 1 standard deviation
At least
¾ will fall with 2 standard deviations of the mean
At least
8
/
9
will fall with 3 standard deviations of the mean
Generally, for any number
k
greater than 1, at least (11/k
2
) of the measurements will fall within
k
standard deviation of the
mean
Empirical Rule:
Applies only to symmetrical (Normal) bell/mound shaped distributions
Approximate but more precise than Chebyshavs theorem
It apples to population of sample data
Interval
Contains
Approximately 68% of measurements
Approximately 95% of measurements
Approximately 99.7% of measurements
(Almost all)
p
th
percentile p% fall below and (100p)% fall above
zscore Distance between a given measurement x and the mean, expressed in standard deviations
Approximately 68% of measurements Between 1 and 1
(1,1)
Approximately 95% of measurements Between 2 and 2
(2,2)
Approximately 99.7% of measurements Between 3 and 3 (3,3)
Section 3.13.6
Probability Rules for Sample Points (Sample Points The most basic outcome of an experiment):
Let p
i
represent the probability of sample point
i
1.
All sample point probabilities must lie between 0 and 1
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 Fall '09

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