I04-21

Question

The table shows estimates of herbaceous forage production in tons on the National Elk Refuge in Wyoming for 15 years from 1998 to 2012. Forage production measures the amount of food available to elk and bison during a growing season. Herbaceous forage includes vegetation such as grasses, forbs (nonwoody broad-leaved plants), and weeds.
      Year   Grass   Forb   Weed   Total Herbaceous Forage       1998   17,655   1,849   170   19,674       1999   13,904   1,924   0   15,828       2000   9,879   1,304   116   11,299       2001   7,641   1,353   65   9,059       2002   7,980   1,323   228   9,531       2003   5,185   1,007   218   6,410       2004   16,324   2,927   345   19,596       2005   15,881   2,011   98   17,990       2006   12,757   2,523   187   15,467       2007   10,019   1,310   45   11,374       2008   13,087   3,272   57   16,416       2009   15,100   2,524   11   17,635       2010   11,374   2,241   37   13,652       2011   15,677   2,226   4   17,907       2012   9,873   1,800   7   11,680        Annual average     12,156     2,126     106     14,388

For each of the following statements, select  True  if the information in the table accurately supports the statement. Otherwise, select  Not true .

Bunuel · Accepted Answer

Approximate and simplify the numbers where possible. Here's how:

3,272 and 16,416 approximate to 3.2 and 16, giving 20% (since 3.2 is 20% of 16). 
 2,927 and 19,596 approximate to 3 and 20, which is less than 20% (20% would require 4, not 3). 
 2,524 and 17,635 approximate to 2.5 and 18, which is less than 20% (20% would require 3.6, not 2.5).

Continue this way to compare the ratios efficiently without needing exact calculations.

Bunuel · Answer

Official Solution:

Statement 1: 
 
Sort the table by Forbs production. Going through the data, we can easily notice that the year when forbs represented the largest percentage of herbaceous forage was 2008, with 3,272 tons, which was approximately 20%. All other years have a lower percentage. The 3,272 tons of forbs is approximately 50% more than the average of 2,126 for forbs. Therefore, this statement is True.
 
 Statement 2: 
 
The median value for 15 years is the 8th largest value. Sorting the table by Grass, Forb, and Weed production, we find that the medians were 12,757 tons, 1,924 tons, and 65 tons, respectively. Meanwhile, the averages for Grass, Forb, and Weed were 12,156 tons (less than the median), 2,126 tons (greater than the median), and 106 tons (greater than the median), respectively. Therefore, this statement is False.
 
 Statement 3: 
 
Two data sets are positively correlated if they both tend to be higher in the same cases. They are negatively correlated if one tends to be higher in cases where the other is lower. For positively correlated data, their lines tend to slope up or down together; the more consistently this happens, the stronger the positive correlation. Conversely, when two data sets are negatively correlated, the line for one tends to slope up while the other slopes down, and vice versa. The more consistently these opposite slopes occur, the stronger the negative correlation.
 
Examining Grass production and Total Herbaceous Forage production over the years, we observe that in most cases, when one increases, the other also increases. This indicates that, if anything, these data are positively correlated. Therefore, this statement is False.

Correct answer:

Forbs production in the year when forbs represented the largest percentage of herbaceous forage was more than 30% higher than the average forbs production.  "True"

The median production value for each of Grass, Forb, and Weed was greater than the corresponding average production.  "False"

The table shows a negative correlation between Grass production and Total Herbaceous Forage production over the years.  "False"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

chai9944 · Answer

Sort the table by Forbs production. Going through the data, we can easily notice that the year when forbs represented the largest percentage of herbaceous forage was 2008, with 3,272 tons, which was approximately 20%. All other years have a lower percentage. The 3,272 tons of forbs is approximately 50% more than the average of 2,126 for forbs. Therefore, this statement is True.

I wanna know any tricks, so that I could get an idea, which one has the hoghest/lowest ppercentage, by quickly glancing

I wanna know any tricks, so that I could get an idea, which one has the hoghest/lowest ppercentage, by quickly glancing

pk3329 · Answer

I like the solution - it’s helpful.

goonjoon · Answer

I don’t quite agree with the solution. For the first T/F one, the wording is a bit weird in the sense that it can be interpreted as when forbs made up the greatest percentage of the herbaceous forage

Bunuel · Answer

The wording is clear and unambiguous. There is only one sensible, correct reading: “forbs represented the largest percentage of herbaceous forage” means the forbs share of the total herbaceous forage, that is forbs divided by (grass + forbs + weed), which is the same as forbs divided by Total Herbaceous Forage.

I04-21

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My Rewards

Year	Grass	Forb	Weed	Total Herbaceous Forage
1998	17,655	1,849	170	19,674
1999	13,904	1,924	0	15,828
2000	9,879	1,304	116	11,299
2001	7,641	1,353	65	9,059
2002	7,980	1,323	228	9,531
2003	5,185	1,007	218	6,410
2004	16,324	2,927	345	19,596
2005	15,881	2,011	98	17,990
2006	12,757	2,523	187	15,467
2007	10,019	1,310	45	11,374
2008	13,087	3,272	57	16,416
2009	15,100	2,524	11	17,635
2010	11,374	2,241	37	13,652
2011	15,677	2,226	4	17,907
2012	9,873	1,800	7	11,680
Annual average	12,156	2,126	106	14,388

True	False
		Forbs production in the year when forbs represented the largest percentage of herbaceous forage was more than 30% higher than the average forbs production.
		The median production value for each of Grass, Forb, and Weed was greater than the corresponding average production.
		The table shows a negative correlation between Grass production and Total Herbaceous Forage production over the years.