With reference to this table, a statistician has proposed the followin

Lets go Category wise from lowest to highest: Typical Countries.
Land Area: Australian Capital Territory, Tasmania, Victoria, New South Wales, South Australia, Northern Territory,Queensland, Western Australia.
Population: Northern Territory, Australian Capital Territory, Tasmania, South Australia, Western Australia, Queensland, Victoria, New South Wales.
Population Density: Northern Territory, Western Australia, South Australia, Queensland, Tasmania, New South Wales, Victoria, Australian Capital Territory.
% of Population in capital: Tasmania, Queensland, Northern Territory, New South Wales, Victoria, Western Australia,South Australia, Australian Capital Territory.

Now 25% of 8 = 2.
1. New South Wales is typical in more categories than any other listed state/territory.
Now we can see from above that New South Wales, is typical only in Population, so
Answer No..

I think the OA for 2nd should also be No, since New South Wales is geographically typical equal as compared to South Australia.
SajjadAhmad, kindly correct me if I am wrong.
2. No listed state/territory is more geographically typical than South Australia.
As we can see that New South wales is equally typical, so
Answer - No.


3. The Australian Capital Territory is not typical in any of the categories.
As we can in the data in bold above, we can see that Australian Capital Territory is not typical in any of the categories, so
Answer - Yes

Very Interesting Set, Kudos for that one. Answers as No, Yes and Yes

Logic Building :
1) 25% means 2 states on each side
2) There are 8 states, so typical means 3-6th positions in that category.



Statement 1 : New South Wales is typical in more categories than any other listed state/territory.
We check the 1st category: 4th place : typical
2nd category: 8th place : not typical
3rd category: 6th place: typical
4th category: 4th place: typical.
So 3 categories. We quickly check other territories and reject those who are not typical in at least 2 categories. After this South Australia is also typical in 3 categories.

Statement 2 : No listed state/territory is more geographically typical than South Australia.

From the first statement, we know that SA is equally typical in 3 categories. The wording states that SA should be maximum and it is (even though it shares that spot with South Wales

Statement 3 : The Australian Capital Territory is not typical in any of the categories.
On a quick glance, we see that ACT is always in the highest/lowest places. So this is true.

1)No,In terms of Land area New South Wales is on 4th rank,
In terms of Population New South Wales is on 8th rank,
In terms of Population density New South Wales is on 5th rank,
In terms of % population New South Wales is on 4th rank,

So it is typical in 3 categories but South Australia is also typical in 3 categories

B)Yes,since South Wales is equal in terms of that criteria

C)Yes,Since Australian capital territory is twice in top 2 and twice in bottom 2 so it is not typical

Posted from my mobile device

­Could someone please explain the logic of typical states lying in row 3-6? Why can't they be in row 4 and 5, with 3 above and 3 below. That would also count as the median, right? There's something I'm not able to understand in the conditions given in the question for a state qualifying as typical. Please help.

"For each of the four categories of statistics, a state/territory is typical if and only if it is among the 50% of listed states and territories that are closest to the median value for that category. For any two listed states and territories, if one is typical in a greater number of categories than the other, the former is to be considered more geographically typical than the other."

ACT3010 Notice that your prompt is different than the original post. I have the same as yours and got the 3rd question wrong and am trying to understand why. To restate it, the question in my OG package is all the same except for the measure of criteria. To restate it, the question has changed by saying:

For each of the four categories of statistics, a state/territory is typical if and only if it is among the 50% of listed states and territories that are closest to the median value for that category. For any two listed states and territories, if one is typical in a greater number of categories than the other, the former is to be considered more geographically typical than the other.

This is quite different. For calculating the median, I am sorting by column and taking the average of position 4 and 5. Then, I find the 4 closest to that median value. So for Population:
(1601800 + 2163200)/2 = 1882500.

For the third yes/no question:
The Australian Capital Territory is not typical in any of the categories.

This is where I think it differs from the original posted based on the definition of 'typical'

Southern Australia and Western Australia are easy to see they are 'typical' so that is 2 of the 4. It's also easy to see that Victoria and New South Wales are 'not typcial' by just a glance. For the remaining I did the math:

Tasmania:
1882500-498200 = 1,384,300

Queensland:
4279400 - 1882500 = 2,396,900

(we now know that Tasmania makes the 3rd of the 4 typical)

Australian Capital Territory:
1882500-34200 = 1,848,300

Since ACT is closer to the median than Queensland, according to the definition I provided above for typical, this SHOULD be typical making the answer "No" since the statement does not match the statement...

However, the OG still says this is "Yes" with the provided explanation:
----
RO3: Apply

The Australian Capital Territory does not appear in the table of typical states and territories produced in the analysis of RO1. Therefore the Australian Capital Territory is not typical in any category.

The correct answer is Yes.
----

If I have made an error, feel free to correct me.

We have 8 states given. Also given "a state/territory is typical if and only if it is neither among the 25% of listed states/territories with the least values for that category nor among the 25% of listed states/territories with the greatest values for that category."

This means that a state is typical only if it it is neither in the top 2 (25% of 8) and nor in the bottom 2 when you sort by any category. So it is typical if it lies in one of the middle 4 rows.

New South Wales is typical in more categories than any other listed state/territory

So New South Wales (NSW) is typical if it lies within the mid 4 rows (neither top 2 nor bottom 2) for the category.

Sort by all 4 categories and note that NSW is typical in 3 of them - Land Area, Pop density and %Pop in capital. So we need to find if any other state is typical in 3 or more categories.

Sort by Land Area - Typical are NSW, V, SA, NT
Sort by Population - SA is still typical here. V and NT are not.
Sort by Population Density - SA is still typical.

This means NSW is NOT typical more categories than SA. SA is also typical in at least 3 categories. No state is typical in all 4 categories.
Select No

No listed state/territory is more geographically typical than South Australia.

We already have the answer to this. SA is typical in 3 categories and no state is typical in more than 3.
Select Yes

The Australian Capital Territory is not typical in any of the categories.

Quick sort all 4 categories. ACT is not in the mid 4 rowsl in any.

Select Yes

Here is a discussion on another table question: https://youtu.be/UtEAoNLP4dw






The point of this question is quick sorting.

I agree here