Noob problem: comparing two datasets- Acreage and Yield such that Acreage * Yield = Production.

[Zombie1982]

So my first post here and I think this is a pretty dumb problem and there's something very obvious I'm missing. However, after scratching my head for more than a day, I decide to seek community help solving this.

I am comparing two datasets- Acreage and Yield such that Acreage * Yield = Production. Consider the following table:

S.no	State	Acerage 2022 (Ha)	Acerage 2023 (Ha)	% Change Acerage	Yield 2022 (MT/Ha)	Yield 2023 (Mt/Ha)	% Change Yield	Production 2022 (MT)	Production 2023 (MT)	% Change in Production
1	State 1	45,172	38930	-14%	3.2704	2.950	-10%	147,732	114,856	-22%
2	State 2	168,891	57987	-66%	1.5128	1.356	-10%	255,502	78,613	-69%
3	State 3	188,911	69091	-63%	1.2567	1.084	-14%	237,396	74,885	-68%
4	State 4	33,462	29032	-13%	2.9235	2.827	-3%	97,826	82,060	-16%
5	State 5	41,011	32873	-20%	1.6880	1.580	-6%	69,225	51,946	-25%
6	State 6	21,219	11192	-47%	1.3407	0.900	-33%	28,448	10,073	-65%
	Total	498,666	239,105	-52%	1.677	1.725	3%	836,129	412,433	-51%

So Production for each state is calculated as Acreage * Yield; and for the "Total" (last row), the Average Yield is calculated as Production/Acreage. Now if Yield for 2023 is lower than that of 2022 for every single state, you would expect the Total Yield for 2023 to be lower than that of 2022. Somehow, that's not the case and I'm unable to wrap my head around this.

Any clues about how this is mathematically possible or what am I doing wrong?

Thanks in advance!

 

[Dr.Peterson]

I think what you're observing is similar to this:
https://www.freemathhelp.com/forum/threads/average-hourly-rate-wage-query.135015

What I see in the numbers is that total production decreased a little less than total acreage (percentage-wise), which can happen as a result of the ways the individual decreases lined up. It's not unusual.

 

[Zombie1982]

Thank you Dr. Peterson.
Still trying to wrap my head around this but I appreciate your help pointing me in the right direction.

 

[Dr.Peterson]

Thank you Dr. Peterson.
Still trying to wrap my head around this but I appreciate your help pointing me in the right direction.

One way to try to understand this would be to see if you can make an example with only two states and simple numbers that shows the same behavior. I may try doing that if I have time.

 

[blamocur]

One way to try to understand this would be to see if you can make an example with only two states and simple numbers that shows the same behavior. I may try doing that if I have time.

I went this route but, being lazy, I used random number generator and came up with several examples like the one below. In there I use:

• first characters 'p', 'a' and 'y' for production, acreage and yield respectively
• second characters 'm' and 'n' for states (Maine and Nevada ?
• third characters '1' and '2' for the first and second years respectively
• 'y1' and 'y2' stand for total yields.

pm1 480 pm2 633 am1 566 am2 744 ym1 0.8481 ym2 0.8508
pn1 1935 pn2 1425 an1 1387 an2 1011 yn1 1.3951 yn2 1.4095
y1 1.2366 y2 1.1726 1.0545

 

[Dr.Peterson]

I went this route but, being lazy, I used random number generator and came up with several examples like the one below. In there I use:

• first characters 'p', 'a' and 'y' for production, acreage and yield respectively
• second characters 'm' and 'n' for states (Maine and New Hampshire?
• third characters '1' and '2' for the first and second years respectively
• 'y1' and 'y2' stand for total yields.

pm1 480 pm2 633 am1 566 am2 744 ym1 0.8481 ym2 0.8508
pn1 1935 pn2 1425 an1 1387 an2 1011 yn1 1.3951 yn2 1.4095
y1 1.2366 y2 1.1726 1.0545

I put that into my copy of the spreadsheet:

S.no​	State​	Acreage 2022 (Ha)​	Acreage 2023 (Ha)​	% Change Acreage​	Yield 2022 (MT/Ha)​	Yield 2023 (Mt/Ha)​	% Change Yield​	Production 2022 (MT)​	Production 2023 (MT)​	% Change in Production​
1​	State 1​	566​	744​	31%​	0.8481​	0.8508​	0.32%​	480​	633​	31.88%​
2​	State 2​	1,387​	1011​	-27%​	1.3951​	1.4095​	1.03%​	1,935​	1,425​	-26.36%​
	Total​	1,953​	1,755​	-10%​	1.2366​	1.1726​	-5.17%​	2,415​	2,058​	-14.78%​

I see that the yield increased in each state, but the overall yield decreased. Acreage and production increased in state 1, but decreased in (larger) state 2; this is a little different from the original, but may only make the effect more pronounced, rather than being a major difference.

Now we can ponder the actual cause of the phenomenon.

(What is your last number, 1.0545? I don't see that in my table.)

 

[Dr.Peterson]

I played with it manually and got this example:

S.no​	State​	Acreage 2022 (Ha)​	Acreage 2023 (Ha)​	% Change Acreage​	Yield 2022 (MT/Ha)​	Yield 2023 (Mt/Ha)​	% Change Yield​	Production 2022 (MT)​	Production 2023 (MT)​	% Change in Production​
1​	State 1​	20​	10​	-50.00%​	7.5000​	10.5000​	40.00%​	150​	105​	-30.00%​
2​	State 2​	110​	100​	-9.09%​	1.0909​	1.1500​	5.42%​	120​	115​	-4.17%​
	Total​	130​	110​	-15.38%​	2.0769​	2.0000​	-3.70%​	270​	220​	-18.52%​

Here's a graphical view:



A is state 1, B is state 2, and C is the totals. The slope of each arrow is the yield; you can see that the yields of both A and B increased, but the total yield decreased. Making changes in the GeoGebra graph makes it clear that the slopes can vary wildly.

 

[blamocur]

(What is your last number, 1.0545? I don't see that in my table.)

It's y2/y1.