The question asks to find $ \chi^{2*} $ that cuts off 5% of the tail with df=52. the chart given lists df=50 then jumps to 60
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I would take the data from df=50 in this case. If it was 55--> average
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(-1) This is not interpolation at all. If you're going to average for $df=55$, which is (linear) interpolation, then why not linearly interpolate for $df=52$? Why introduce such an inconsistency, especially when the error made when replacing $52$ by $50$ is substantial? – whuber Nov 25 '15 at 22:03
*from your body text as well. Your question is covered in the answer here: How do I find values not given in (interpolate in) statistical tables? – Glen_b Nov 25 '15 at 21:53