# Quod Erat Demonstrandum

## 2008/01/25

### [CE][Math] Statistics: More dispersed?

Filed under: HKCEE — johnmayhk @ 2:52 下午

In CE mathematics, we know that there are at least 3 measurements for dispersion, namely, range, inter-quartile range and standard derivation.

Describing or comparing the dispersion of different sets may be a very important application.

About the standard derivation, you may read my old messages for your reference
http://www.hkedcity.net/ihouse_tools/forum/read.phtml?forum_id=27877¤t_page=&i=1159940&t=1159940&v=t
http://www.hkedcity.net/ihouse_tools/forum/read.phtml?forum_id=27877¤t_page=&i=965435&t=959956

Given two numerical data sets A and B.

If we come across the following situations

range of A > range of B and
inter-quartile range of A < inter-quartile range of B

How to compare which set is more dispersed?

Well, you may say, just look at the standard derivation.

OK. If we have the following

range of A > range of B and
inter-quartile range of A > inter-quartile range of B and
standard derivation of A < standard derivation of B

Is it true to draw the conclusion that set B is more dispersed?

Further, how about when (set A $\ne$ set B) such that

range of A = range of B and
inter-quartile range of A = inter-quartile range of B and
standard derivation of A = standard derivation of B

Urm, let me give the following as an example

Set A ={1,10,10,10}
Set B = (1,1,1,10}

Is it true to draw the conclusion that both sets have the same dispersion?

The problem may be something about the vagueness of the concept of “dispersion". How to resolve it?

## 2 則迴響 »

1. Give Wong Chi Ho a chance to perform la, this might be his ever-lasting memory!
I attempt to read it, and I do, but I know not a word you’retalking about!
Without you in the critical thinking class, it is a ‘living market’….

迴響 由 Edmund To — 2008/01/25 @ 9:57 下午 | 回應

2. Yes, I do hope that we could enjoy Raymond’s performance during Talentine.

You’d attempted to read this post? Although it’s at F.5 level, after introducing some easy concepts, it is extremely easy to understand.

A living market? That’s horrible. However, I just wanna know, do you really learn something from the class? Had you ever applied the materials about critical thinking in your daily life?

迴響 由 johnmayhk — 2008/01/25 @ 11:17 下午 | 回應