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So, let's concentrate, on, say, Kerry's rating.
The poll of 10/15-17 gives him 45%. That's the average of what he got on Oct 15, 16 and 17 respectively. Let's mark these ratings R15, R16 and R17.
We know that (R15 + R16 + R17)/3 = 45. Therefore,
R15 + R16 + R17 = 135
Similarly, (R14 + R15 + R16)/3 = 44. So,
R14 + R15 + R16 = 132
Now, let's look at (R15 + R16) as one variable - call it X.
X + R17 = 135, and X + R14 = 132.
So, now we also know that
R17 = R14 + 3
In other words, his rating on the 17th was higher than on the 14th by 3 points.
Let's take another sample:
(R13 + R14 + R15)/3 = 44.
Therefore,
R13 + R14 + R15 = 132
Analogously to what we did last time (take (R14 + R15) as a single variable), we can conclude that
R13 = R16
Repeat the process once more for the 10/12-14 sample, and you'll find out that
R12 = R15
....
You know what man? I was wrong. I've been fucking my brain with this for a few hours now. The problem is that whenever you add an equation to the system, you add a new variable; you can always tell the difference between a certain day and a day 3 days earlier or later, but you can't specifically figure out what exact data is associated with a day. If we had specific data for any day, and for any day not distant from that day by a number of days divisible by 3, we could figure out the whole system. Like, if we had Oct 11th and Oct 15th, we could figure out every day. But this way, we're shit out of luck. Of course, you can make educated guesses. Like, if we assume that Oct 14th and Oct 15th are both 44, then the 17th is 47, and the 13th is also 44, etc.
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