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After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.) for 10 of his clients and checked online price quotes for their policies. The comparisons are shown in the table.

His statistical software produced the following summaries (where PriceDiff = Local - Online):

At first, the insurance agent wondered whether there was some kind of mistake in this output. He thought the Pythagorean Theorem of Statistics should work for finding the standard deviation of the price differences€”in other words, that SD(Local €“ Online) = ˆšSD2(Local) + SD2(Online).

But when he checked, he found that ˆš(229.2812) + (256.2672)2 = 343.864,not 175.663 as given by the software. Tell him where his mistake is.

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