Question

A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the standard deviation of the data. Round your answer to the nearest hundredth, if necessary.

Building Toy Pieces

174	59
279	364
364	59
118	310
279	123
184	522

Answer 1

GIVEN THAT :-

According to the question we have that

the values as

174,279,364,118,279,184,59,364,59,310,123,522

now

TO FIND :- the standard deviation of the data.

FOR FINDING the standared deviation we have a formula

   ==> squreroot (1/N )*sum of all xi*(xi-mean)^2---(1)

where

N =number of variables

xi = values

  

for finding the standared deviation we need to find the mean first

mean = sum of all the values / number of all the values

so ,

174+279+364+118+279+184+59+364+59+310+123+522/12

= 2835/12

therefor MEAN = 236.25

NOw substituting all the values in standared deviation (1) we get

squrerot 1/12((174-236.25)^2+(279-236.25)^2+..........+(522-236.25)^2)

sloving we get that

= squreroot 1/12{(3875.06+1827.56+16320.06+13983.06+1827.56+2730.06+31417.56+16325.06+31417.56+5439.06+12825.56+81653.06)}

= squreroot 1,88,223.66/12

= squre root 15,685.305

=125.2409876997143

therefore,

the standared deviation = 125.24

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