canolrif dosraniad di-or i ddarganfod canolrif hapnewidyn gyda dosraniad di-dor, rydym yn...
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Canolrif Dosraniad Di-or
I ddarganfod canolrif hapnewidyn gyda dosraniad di-dor, rydym yn defnyddio’r ffwythiant dosraniad cronnus F(x).
Mae’r tebygolrwydd fod gan X werth llai na’r canolrif yn 0.5.
P(X ≤ x0.5) = F(x0.5) = 0.5
a b
F(x)
x0
1
0.5
x0.5
The Median of a Continuous Distribution
To calculate the median of a continuous distribution, we must use the cumulative distribution function F(x).
The probability that X has a lower value than the median is 0.5.
F(x) = 0 ar gyfer/for x < 0
F(x) = ar gyfer/for 0 ≤ x ≤ 4
F(x) = 1 ar gyfer/for x > 464
3x
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan
Darganfyddwch y canolrif
F(x0.5) = 0.5
5.064
3
x
32645.03 x
17.3323 x
The continuous random variable X is distributed with cumulative distribution function F where
Find the median
Mae’n bosib hefyd defnyddio’r ffwythiant dosraniad cronnus F(x) i ddarganfod amrediad rhyng-chwartel ac amrediad rhyng-ganraddol y dosraniad.
Mae’r tebygolrwydd fod gan X werth llai na’r chwartel isaf yn 0.25.
P(X ≤ x0.25) = F(x0.25) = 0.25
a b
F(x)
x0
1
0.25
x0.25
Mae’r tebygolrwydd fod gan X werth llai na’r chwartel uchaf yn 0.75.
P(X ≤ x0.75) = F(x0.75) = 0.75
a b
F(x)
x0
10.75
x0.75
Yr Amrediad rhyng-chwartel – The inter-quartile range
It is also possible to use the cumulative distribution function F(x) in order to calculate the inter-quartile range and the inter-percentile range of the distribution.
The probability that X has a lower value than the lower quartile is 0.25.
The probability that X has a lower value than the upper quartile is 0.75.
F(x) = 0 ar gyfer/for x < 0
F(x) = ar gyfer/for 0 ≤ x ≤ 4
F(x) = 1 ar gyfer/for x >
4
64
3x
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir gan
Darganfyddwch yr amrediad rhyng-chwartel
F(x0.75) - F(x0.25)
75.064
3
x
486475.03 x
63.348375.0 x
F(x0.75) = 25.064
3
x
166425.03 x
52.216325.0 x
F(x0.25) =
Amrediad rhyng-chwartel = 3.63 – 2.52 = 1.11
The continuous random variable X is distributed with cumulative distribution function F where
Calculate the inter-quartile range.
Inter-quartile range =
Yr Amrediad rhyng-ganraddol - The inter-percentile range
Darganfyddwch yr amrediad rhyng-ganraddol 10-90
F(x0.9) - F(x0.1)
9.064
3
x
6.57649.03 x86.36.573
75.0 x
F(x0.9) = 1.064
3
x
4.6641.03 x
86.14.6325.0 x
F(x0.1) =
Amrediad rhyng-ganraddol 10-90 =3.86 – 1.86 = 2
F(x) = 0 ar gyfer/for x < 0
F(x) = ar gyfer/for 0 ≤ x ≤ 4
F(x) = 1 ar gyfer/for x >
4
64
3x
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad cronnus F a roddir ganThe continuous random variable X is distributed with cumulative distribution function F where
Calculate the inter-percentile range 10-90
The inter-percentile range 10-90 =
Ymarfer Canraddau/Percentile Exercise
Gwaith Cartref/Homework 13