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Statistics
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01:960:401
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Micheal Miniere
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Lecture 2

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Statistics

01:960:401

Micheal Miniere

Summer

Description

where i goes from 1 to N
Interpreting the standard deviation:
Empirical Rule: If the data has a bell-shaped histogram, then
1) About 68% of all data values fall within one standard deviation of the mean
2) About 95% of all data values fall within two standard deviations of the mean
3) About 99.7% of all data val
fall within three standard deviations of the mean
Chebyshev's Rule: (for any shape of the distribution)
1) At least 75% (3/4) of all the data values fall within two standard deviations of the mean.
2) At least 89% (8/9) of all data values fall within three standard deviations of the mean.
Actual formula for Chebyshev's Theorem:
Given a real number k 1 nd given any set of numbers, the proportion (or fraction) of thos
numbers that lie within k standard deviations of the mean is at least 1--
of all data values lie within two standard deviations of the
Note if k 2, then at least 1
mean as stated above, and if k
3, then at least 1-
of all data values lie within three
standard deviations of the mean as stated above
Definition: The z-score is the number of standard deviations between a given value of x in a
data set and the
mean. It is found by using the following formula
for the sample and for the population.
If z 0, then
x is above the mean. If 0, then x is below the mean.
Rule of thumb for typical sets
Usual values:
Unusual
values: z 2
We will do some examples in class.
G-dividus the lower haly of data set in mall/Mudian data hillw Ra
ng
A1-mudian
but not intluding
Auartit exampks
data sut: l, 2
2,3, 4,5, e, h, g ,ll,13
calculator: daa in LI hit 3Pat Calc
calculat
n,GI, max 5 numbr summlr
ada
sut: bb, 10,bq,80, 60, h7,72,73,70,57,h3,10, 38,17, 53, 7, 75, 70
7b, 74, 75, 7b
ed an as at
outlier and loninil
50
54.25
August H smallest
ran
where i goes from 1 to N Interpreting the standard deviation: Empirical Rule: If the data has a bell-shaped histogram, then 1) About 68% of all data values fall within one standard deviation of the mean 2) About 95% of all data values fall within two standard deviations of the mean 3) About 99.7% of all data val fall within three standard deviations of the mean Chebyshev's Rule: (for any shape of the distribution) 1) At least 75% (3/4) of all the data values fall within two standard deviations of the mean. 2) At least 89% (8/9) of all data values fall within three standard deviations of the mean. Actual formula for Chebyshev's Theorem: Given a real number k 1 nd given any set of numbers, the proportion (or fraction) of thos numbers that lie within k standard deviations of the mean is at least 1-- of all data values lie within two standard deviations of the Note if k 2, then at least 1 mean as stated above, and if k 3, then at least 1- of all data values lie within three standard deviations of the mean as stated above Definition: The z-score is the number of standard deviations between a given value of x in a data set and the mean. It is found by using the following formula for the sample and for the population. If z 0, then x is above the mean. If 0, then x is below the mean. Rule of thumb for typical sets Usual values: Unusual values: z 2 We will do some examples in class. G-dividus the lower haly of data set in mall/Mudian data hillw Ra ng A1-mudian but not intluding Auartit exampks data sut: l, 2 2,3, 4,5, e, h, g ,ll,13 calculator: daa in LI hit 3Pat Calc calculat n,GI, max 5 numbr summlr ada sut: bb, 10,bq,80, 60, h7,72,73,70,57,h3,10, 38,17, 53, 7, 75, 70 7b, 74, 75, 7b ed an as at outlier and loninil 50 54.25 August H smallest ranStandard
on
ata sit:
ths us now tu data valus bl) dihr from the man
to Drminties noth
f data bell-s
689,
X-25
amouMM
that into
St. tons
or any distribution shape
amount of data
that into
3s
populatlan
amp
Z-score:
-tells how many st diviations thort art blw X and X
wnnt X is any number
x wli t2 st. alviations man 7usual
lo12llb
Similar iksts art given to 2 groups,bud the tests have
Tes
A B Which is a betttr store 2
a on trst A or 29 on B?
M 20
St. dev over thi mlun.
th is betttr? a 30 on ttst A or a q on test B
mean
Standard on ata sit: ths us now tu data valus bl) dihr from the man to Drminties noth f data bell-s 689, X-25 amouMM that into St. tons or any distribution shape amount of data that into 3s populatlan amp Z-score: -tells how many st

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