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Statistics Notes: Measures of Spread ­ Standard Deviation
October 22, 2015
I shared student responses to the exit slip.
Statisticians usually use Standard Deviation rather than MAD to calculate variance. Calculating the standard deviation is similar to calculating the MAD.
Example: the data in the table represents the number of home runs hit by several teams in the American League in 2001.
Find the MAD and the Standard Deviation for the data.
Population Variance:
Population Standard Deviation:
Sample Variance:
Sample Standard Deviation:
p135 for why n ­ 1.
sample standard deviation
dividing by n ­ 1.
dividing by n
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Statistics Notes: Measures of Spread ­ Standard Deviation
October 22, 2015
Empirical Rule or the 68­95­99.7 Rule
The curve of the graph of a normal distribution is:
1. Symmetric
2. Maximized at the mean x
3. 68% of the data is within 1 σ of the x
4. 95% of the data is within 2 σs of the x
1σ
5. 99.7% of the data is within 3 σs of the x
x
68%
95%
99.7%
The weight, in grams, of both kidneys based upon a random sample of 60 normal men aged 40 ­ 49 resulted in a mean of 325 grams, with a standard deviation of 30 grams. A histogram of the data indicates that the data approximates a normal distribution.
What percent of the kidneys weigh within 3 standard deviations of the mean?
x
What percent of the kidneys weigh between 265 and 385 grams?
Chebyshev's Theorem
For any data set, regardless of the shape of the distribution, at least
of the data will lie within k standard deviations of the mean where k > 1.
Using Chebyshev's theorem, what percent of the kidneys weigh within 3 standard deviations of the mean?
What percent of the kidneys weigh between 265 and 385 grams?
HW: p141 C&V #1
p142 #3, 5, 21, 23, 25, 32
2