Online insurance I 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 below. His statistical software produced the following summaries (where Price Diff = 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) = ˆš (SD2(Local) + SD2(Online).)
But when he checked, he found that
ˆš ((229.28l) 2 + (256.267)2) = 343.864, not 175.663
as given by the software. Tell him where his mistake is.

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VariableCount Local Online PriceDiff StdDev 799.200 229.281 753.300 256.267 45.9000 75.663 Mean 10 10 10 Local Online PriceDiff 568 391 872 602 270 451 488 37 1229 903 326 72 1021 1270 249 80 605 677 783 703 844 789 907 1008101 712 702 10