Transcript Document

Canolrif Dosraniad Di-or
The Median of a Continuous Distribution
I ddarganfod canolrif hapnewidyn gyda dosraniad di-dor,
rydym yn defnyddio’r ffwythiant dosraniad cronnus F(x).
To calculate the median of a continuous distribution, we must use
the cumulative distribution function F(x).
Mae’r tebygolrwydd fod gan X werth llai na’r canolrif yn 0.5.
The probability that X has a lower value than the median is 0.5.
P(X ≤ x0.5) = F(x0.5) = 0.5
F(x)
1
0.5
0
a
x0.5 b
x
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant
dosraniad cronnus F a roddir gan
The continuous random variable X is distributed with cumulative
distribution function F where
F(x) = 0
x3
F(x) =
64
F(x) = 1
ar gyfer/for x < 0
ar gyfer/for 0 ≤ x ≤ 4
ar gyfer/for x > 4
Darganfyddwch y canolrif
Find the median
F(x0.5) = 0.5
x3
 0 .5
64
x 3  0.5  64  32
x  3 32  3.17
Mae’n bosib hefyd defnyddio’r ffwythiant dosraniad cronnus F(x) i
ddarganfod amrediad rhyng-chwartel ac amrediad rhyng-ganraddol y
dosraniad.
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.
Yr Amrediad rhyng-chwartel – The inter-quartile range
Mae’r tebygolrwydd fod gan X
werth llai na’r chwartel isaf yn
0.25.
Mae’r tebygolrwydd fod gan X
werth llai na’r chwartel uchaf yn
0.75.
P(X ≤ x0.25) = F(x0.25) = 0.25
P(X ≤ x0.75) = F(x0.75) = 0.75
The probability that X has a lower
value than the lower quartile is 0.25.
F(x)
1
The probability that X has a lower
value than the upper quartile is 0.75.
F(x)
1
0.75
0.25
0
a
x0.25
b
x
0
a
x0.75b
x
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad
cronnus F a roddir gan
The continuous random variable X is distributed with cumulative
distribution function F where
F(x) = 0
x3
F(x) =
64
F(x) = 1
ar gyfer/for x < 0
ar gyfer/for 0 ≤ x ≤ 4
ar gyfer/for x > 4
Darganfyddwch yr amrediad rhyng-chwartel
Calculate the inter-quartile range.
F(x0.75) - F(x0.25)
x3
F(x0.75) =
 0.75
64
3
x  0.75 64  48
x0.75  3 48  3.63
Amrediad rhyng-chwartel =
Inter-quartile range =
x3
F(x0.25) =
 0.25
64
3
x  0.25 64  16
x0.25  3 16  2.52
3.63 – 2.52 = 1.11
Yr Amrediad rhyng-ganraddol - The inter-percentile range
Dosrennir yr hapnewidyn di-dor X gyda ffwythiant dosraniad
cronnus F a roddir gan
The continuous random variable X is distributed with cumulative
distribution function F where
F(x) = 0
ar gyfer/for x < 0
x3
F(x) =
64
ar gyfer/for 0 ≤ x ≤ 4
F(x) = 1
ar gyfer/for x > 4
Darganfyddwch yr amrediad rhyng-ganraddol 10-90
Calculate the inter-percentile range 10-90
F(x0.9) - F(x0.1)
3
x
F(x0.9) =
 0 .9
64
x3  0.9  64  57.6
x0.75  3 57.6  3.86
3
x
F(x0.1) =
 0.1
64
x3  0.1 64  6.4
x0.25  3 6.4  1.86
Amrediad rhyng-ganraddol 10-90 =
The inter-percentile range 10-90 =
3.86 – 1.86 = 2
Ymarfer Canraddau/Percentile Exercise
Gwaith Cartref/Homework 13