Let's say the average height of people is 150cm, with a std dev of 20cm, and their heights are normally distributed. Now if I group these people randomly in groups of 6 people, and I just take the height of the shortest person in each group. What is the mean and std dev of these shortest people?
2007-08-12 21:27:38 · 4 answers · asked by peaceharris 2 in Science & Mathematics ➔ Mathematics
This is "Order Statistics"
It is straigthforward to write the expression of the mean and variance but the computation is to be given to a math engine (MATLAB is my prefered)
2007-08-12 21:44:46 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Are you speaking approximately variance or nicely-known deviation? One is the sq. root of the different. If the advise is sixteen.2 and the SD is a million.5625 then you definately desire the table or graph of the section below the conventional Distribution curve to respond to those. yet devoid of understanding the SD you could no longer answer something.
2016-11-12 04:36:48 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Without doing any maths, I would guess that the mean would be 147 cm and the standard deviation would remain same. But I could be wrong since I left statistics long ago.
2007-08-12 21:33:23 · answer #3 · answered by Swamy 7 · 0⤊ 0⤋
The cumulative distn of the minimum is 1-[1-F(x)]^6 and its pdf is 6{[1-F(x)]^5}f(x), where F(x) is the normal cdf and f(x) is normal pdf.
You can use either the cdf or pdf to derive the mean and variance.
2007-08-13 00:46:09 · answer #4 · answered by Anonymous · 0⤊ 0⤋