Home > Graphics > $50k < $40k < $75k ?

$50k < $40k < $75k ?

Kiplinger has a new-ish infographic concerning retirement savings.  It’s not good.  The infographic is here, and is linked from here.  It’s comprised of four graphs. The first, and most error-laden, is below.

I count 13 errors.

1. The horizontal scale changes.  The differences between the lines, from left to right, are $4k, $5k, $5k, $10k, $25k, $25k, $25k, $400k, $500k.  This scale is not just unusual, it is inconsistent. (Here is a possibly-too-technical way to say the scale is inconsistent: in math terms, thinking of the scale as a function, either 1) the scale is not smooth, or 2) the second derivative of the scale changes sign.)

2. The orange set of bars partially covers the green set.  The size of the bar as we see it should always correspond to the amount depicted.  In the graph above, the size of the green bar does not correspond to the dollar amount; it corresponds to the larger amount minus the smaller amount.  (Or, that’s what it’s meant to be. See errors 4-13 below.)

3. The baseline for the bars, $1000, is arbitrary.  Why not start at $0?

Now, from here on out, it’s individual errors of the same kind over and over: some bars are longer than they should be, some shorter.

4. Look at the orange bars for 1920 and 1930.  They are the same size, but the amounts are different, $3,729 and $3,114.  (And the bars are the same size, not just similar.)  In case you might think this is just because the amounts are close: The difference in amounts is $3,729 – $3,114 = $615.  The 1930 and 1940 orange bars are clearly not the same size, even thought the difference in dollars is smaller: $3,114 – $2,610 = $504.

5. and 6. The 1950 bars are the wrong size. The orange bar, depicting $4,493 lies between the line for $5k and $10 (so $5k < $4 < $10k ?).  The green bar depicting $112,335 is too short because it falls between $75k and $100k.

And so on.

7. The 1930 green bar is too short.
8. The 1960 green bar is too short.
9. The 1970 green bar is too short.
10. The 1980 orange bar is too long.
11. The 1990 orange bar is too long.
12. The 1990 green bar is too short.
13. The 2010 orange bar is too long.

It could be that all of the errors 4-13 happened because the scale is inconsistent.  If the scale did not vary so much, perhaps the graph maker would have noticed bars with the wrong length.  Who knows?

I would bet that the number of errors is greater than 13, but I’m only reporting the ones I can be sure of.  For instance, look at the orange bar for 2000, which terminates closer to $50k than $25k. If the scale is linear between $25k and $50k, then the bar should terminate closer to $25k, because 32 – 25 = 7 and 50 – 32 = 18.  If the scale is log (multiplicative) between $25k and $50k, then $32k should still terminate closer to $25k since 32/25 = 1.28 and 50/32 = 1.5525.  Thus I also suspect the 2000 orange bar is too long, but I can’t be sure because I don’t know what the scale is.

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Categories: Graphics
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