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Here are the prices of five new pairs of hockey skates, in dollars: 59, 60, 65, 99, 175.The standard deviation is about $49.If a sixth pair of skates is added to the data that has a price of $450, what happens to the standard deviation?A.The new standard deviation is greater than $49.B.The new standard deviation is $499.C.The new standard deviation is less than $49.D.The standard deviation is still $49.SUBMITarrow_backPREVIOUS

Question

Here are the prices of five new pairs of hockey skates, in dollars: 59, 60, 65, 99, 175.The standard deviation is about 49.Ifasixthpairofskatesisaddedtothedatathathasapriceof49.If a sixth pair of skates is added to the data that has a price of 450, what happens to the standard deviation?A.The new standard deviation is greater than 49.B.Thenewstandarddeviationis49.B.The new standard deviation is 499.C.The new standard deviation is less than 49.D.Thestandarddeviationisstill49.D.The standard deviation is still 49.SUBMITarrow_backPREVIOUS

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Solution

The standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean (average) value, while a high standard deviation means that the values are spread out over a wider range.

In this case, adding a sixth pair of skates that has a price of 450,whichissignificantlyhigherthantheotherprices,willincreasethedispersionorspreadofthedata.Therefore,thenewstandarddeviationwillbegreaterthantheoriginalstandarddeviationof450, which is significantly higher than the other prices, will increase the dispersion or spread of the data. Therefore, the new standard deviation will be greater than the original standard deviation of 49.

So, the correct answer is A. The new standard deviation is greater than $49.

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