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

Question

With reference to this table, a statistician has proposed the following criteria for determining the “most geographically typical” of the listed Australian states/territories:

State/territory  
  Land area
(km^2)  
  Population
(2006)  
  Population density
(people/km^2)  
  % of population
in capital  
 
  Australian Capital
Territory  
 2358 
 344200 
 137.53 
 99.6 
 
  New South Wales 
 800642 
 6967200 
 8.44 
 63 
 
  Northern Territory 
 1349129 
 219900 
 0.15 
 54 
 
  Queensland 
 1730648 
 4279400 
 2.26 
 46 
 
  South Australia 
 983482 
 1601800 
 1.56 
 73.5 
 
  Tasmania 
 68401 
 498200 
 7.08 
 41 
 
  Victoria 
 227416 
 5297600 
 22 
 71 
 
  Western Australia 
 2529875 
 2163200 
 0.79 
 73.4

For each of the four categories of statistics, 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.

For each of the following statements, select  Yes  if the statement is accurate based on the statistician’s criteria; otherwise select  No .

egmat · Accepted Answer

This TA question comes with a simple table but an involved translation. To solve it efficiently, you need to:
 
 Translate the definition of “typical” into simpler terms using the strategic pausing technique. Doing this upfront ensures that evaluation of the statements is not a time hog. 
 Make inferences when direct information is not provided. This is true about statement 2 in the question in which we needed to extend the given definition of “typical” to find the “most geographically typical” state/territory. 
 Determine the approach to evaluate each statement before plunging into the 32 data points in the table. This is to keep you focused on just what is needed. Observe how we used tally marks to solve one of the statements and how that same tally chart was used in the rest of the statements as well. So, do not shy away from doing the work that is expected to answer each statement. And do not think that same amount of work will be required for all statements. Be open to reusing the analysis that you have done for the statements.

As you watch the video solution, observe how absolute comfort in how to work with a table in a TA question is imperative for our goal of “owning the dataset”. Here, you sort by not one or two but all 4 columns to infer the information that is then used in each statement. Call the analysis of this question done once you have determined why you answered this question incorrectly or why you took longer to answer it. Most likely reasons:
 
 You did not translate the meaning of “typical”. 
 You did not create your own table with tally marks for the states that are “typical”.

https://www.youtube.com/watch?v=FlAvb3SUIQ0

KarishmaB · Answer

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.

gotitright · Answer

KarishmaB

in Q1 here I get that NSW is only once in the top 2, bottom 2 list. So if some there state is 0 times or only 1 time in top 2, bottom 2 list then our answer will be no.

so while I'm sorting and checking for this firstly I have to keep track of what all states are there, then see to it that I have checked for all of them. So how do I do that without listing all the states on paper and then marking how many times have they appeared in top 2, bottom 2 list?

KarishmaB · Answer

You need to find whether any other state is typical in all 4 categories or in 3 categories. 
 
Sort by Land Area - Typical are V, SA, NT (other than NSW)
 So let's track V, SA and NT.

Sort by Population - SA is still typical here. V and NT are not. Now V and NT are relevant only if they are typical in other two categories too.

Sort by Population Density - SA is still typical. We found another state typical in 3 categories.

We don't need to write down anything. You are expected to orally track them. Take reference from the first category sorting. If you find no state, check the last 3 categories to ensure that no state is typical in those 3 alone.

RandyRanderson8 · Answer

KarishmaB

not sure if 2nd one should be no. Just because a territory is typical in most criteria means that no other territory is more typical? The question doesn't clarify that all criteria for identifying as "typical" have equal weightage, no?

Imo, it can be possible that nsw is more typical - especially if the criteria is weighted

KarishmaB · Answer

We have been given the  criteria for determining the “most geographically typical” of the listed Australian states/territories (the 4 given in the table). We have been given how to find whether a territory is "typical" or non-typical for each criterion.

Look at the question stem: For each of the following statements, select  Yes  if the statement is accurate  based on the statistician’s criteria ;

We have been given the statistician's criteria and there is no reason to assume that it is incomplete. When they say "these are his criteria..." we assume that they are giving all the criteria. If we assume that information  could be  missing, then most answers would be CBD and the DI section would make little sense. With practice, the implications of given data will become clear.

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

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State/territory	Land area (km^2)	Population (2006)	Population density (people/km^2)	% of population in capital
Australian Capital Territory	2358	344200	137.53	99.6
New South Wales	800642	6967200	8.44	63
Northern Territory	1349129	219900	0.15	54
Queensland	1730648	4279400	2.26	46
South Australia	983482	1601800	1.56	73.5
Tasmania	68401	498200	7.08	41
Victoria	227416	5297600	22	71
Western Australia	2529875	2163200	0.79	73.4

Yes	No
		New South Wales is typical in more categories than any other listed state/territory.
		No listed state/territory is more geographically typical than South Australia.
		The Australian Capital Territory is not typical in any of the categories.

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