# SOLUTION: for the following data set, approximate the sample standard deviation. miles (per day)---Frequency 1-2--------------- 9 3-4--------------- 22 5-6--------------- 28 7-8----

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: for the following data set, approximate the sample standard deviation. miles (per day)---Frequency 1-2--------------- 9 3-4--------------- 22 5-6--------------- 28 7-8----      Log On

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Question 332582: for the following data set, approximate the sample standard deviation. miles (per day)---Frequency 1-2--------------- 9 3-4--------------- 22 5-6--------------- 28 7-8--------------- 15 9-10-------------- 14Answer by jrfrunner(365)   (Show Source): You can put this solution on YOUR website!Since you dont have the exact value, but instead have a range of values the first thing to do is to get a surrogate (proxy) value. This is usually set a the mid point of the interval 1.5 3.5 etc... --- next set up a data table as follows Let X=midpoint, F=frequency -- X ------ F ---- X*F 1.5 ----- 9 ---- 13.5 3.5 ----- 22 ---- 77.0 5.5 ----- 28 ---- 154.0 7.5 ----- 15 ---- 112.5 9.5 ----- 14 ---- 133.0 --- Compute the average = Xbar = -- for each interval compute a column (Xi-Xbar)^2 and then sum this column =[(1.5-5.57)^2]*9 + [(3.5-5.57)^2]*22 +..+[(9.5-5.57)^2]*14 = 515.59 this sum represents the sum of squared deviations. --- Find the Variance Variance = =515.59/(88-1)=5.926 --- Standard dev = Sqrt(Variance) = Sqrt(5.926)=2.434 === There is another form of the variance formula that you could use Variance =