Graphical representation IR. Need help on one question.

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The scatter plot (attachment) shows the percentage change in median personal income for residents in 30 US states from 2008 to 2009 and from 2009 to 2010. The y-axis represents the percentage change in median income from 2008 to 2009, and the x-axis represents the percentage change in median income from 2009 to 2010.

Q: Among the states represented in the scatter plot above, the number that saw an increase in residents' median income from 2008 to 2009 is_______________the number that saw an increase in residents' median income from 2009 to 2010.

1)smaller than
2)equal to
3)greater than

Please let me know how to approach this IR question. I marked 'greater than' by simply counting the number of dots on the x-axis and y-axis but that is incorrect.

Source: Kaplan CAT.

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by Whitney Garner » Thu Jan 03, 2013 7:49 pm
Hi aman88!

The key to these Graphical Interpretation problems is to make sure you know exactly what the question is asking and translate if necessary. So let's take a look at the specific question and go bit by bit:

"Among the states represented in the scatter plot above,"
- this means we will be using the set of ALL of the dots on the scatterplot

"the number that saw an increase in residents' median income from 2008 to 2009"
- here we should start by reminding ourselves what axis measured the charge from 2008-2009. According to the information given originally, this was the Y_axis (or vertical axis). This means that residents who saw an INCREASE during this period would have POSITIVE Y coordinates (or be located above the x-axis)! Let's count these... we get 10.

"is_______________" (greater, equal to, less than)

- we don't know yet...

"the number that saw an increase in residents' median income from 2009 to 2010."
- So check the original text again to see which axis we use for this range - ah the x-axis. This means that residents who saw an increase during this period would have POSITIVE X coordinates (or be located to the right of the y-axis)! Let's count these... we have 15.

If we put all of this together:

"Among the states represented in the scatter plot above, the number that saw an increase in residents' median income from 2008 to 2009 "is_______________" (greater, equal to, less than) the number that saw an increase in residents' median income from 2009 to 2010."

translates to:
Of all of the dots above, 10 "is_______________" (greater, equal to, less than) 15.

The answer is LESS THAN

Hope this helps!
:)
Whit
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by rtad05 » Tue Jan 29, 2013 8:21 am
Hello,

I am having trouble with this graph as well. But for 2nd question...

"Of the states represented in the scatter plot, _____ had net gain in residents' median income between 2008 and 2010.

What is the strategy to find the answer efficiently and quickly?

After reviewing the answer in Kaplan I am able to get the answer simply with visualization - looking at all the dots in the right lower quadrant and seeing if the gain is larger than the loss. For example, the lowest dot on the right lower quadrant shows that there was about a 9% loss in income for 2008-2009 and roughly a 3.5% gain in income for 2009-2010. So this gives a net loss of 5.5%. Is that the correct way to go about this problem?

Because the answer explanation talks about picking numbers. Is this really necessary to do? And the answer explanation also mentions drawing a line with a -1 slope...is this also necessary?


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by Tommy Wallach » Tue Jan 29, 2013 12:16 pm
Hey rtad05,

Well, obviously any dot in the first quadrant goes in (because those represent a raise/raise). Any dot in the third quadrant is obviously out (because those represent a loss/loss). The tough part is quadrant two and quadrant four.

Anytime the raise is obviously more than the loss, you can count it as a win, and anytime the loss is obviously more than the raise, you'd have to count it as a loss.

If the two were EXACTLY the same, that would count as a loss, because if something goes up and then down (or down and then up) by the same percent, it ends up lower than it started:

100, down by 10% = 90, up by 10% = 99
100, up by 10% = 110, down by 10% = 99

That's why it's helpful to draw the diagonal. Anything above it is a gain, overall. Anything below it is a loss, overall. Anything EXACTLY on the line would be a loss, overall.

Does that make sense? Drawing the line and counting dots shouldn't be particularly time consuming.

-t
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by tanviet » Thu Feb 07, 2013 11:22 pm
understand nothing when I read the question

understand immediately when I read the explanation

Thank you experts.