Friday, September 17, 2010

Ann $450,000Bob $360,000Cal $190,000Dot $210,000Ed $680,000
The table above shows the total sales recorded in July for the 5 salespeople. It was discovered that one of Cal’s sales was incorrectly recorded as one of Ann’s sales. After this error was corrected, Ann’s total sales were still higher than Cal’s total sales, and the median of 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?


fact one: there are an odd number of data points, so the median is actually one of the numbers in the problem. this is cool here, because you know that exactly one of two things has happened: (a) cal's new total is $330,000, (b) ann's new total is $330,000. since none of the other salespeople's totals are going to change, it's impossible for the new median to be anyone's other than ann's or cal's.
fact two: however much you take away from ann's sales, you have to add to cal's sales. you're basically just exchanging money between the two of them, so whatever dollars you take away from ann must go to cal.
fact three: in any problem like this one, you should put the salary figures in order. this goes without saying in any problem that has to do with the median of a set

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