Who is Paying More at the Pump? The prices below are for regular gasoline (per l
ID: 2972256 • Letter: W
Question
Who is Paying More at the Pump? The prices below are for regular gasoline (per litre) as of 6/28/2009, 4:17:51 PM local time. Find the standard deviation of these values. Find the range R. Compare the range and the standard deviation. Is range related to standard deviation, in any sense? Use range to approximate the standard deviation. Is this a good approximation? Subtract 0.5 from every observation and calculate the variance for the original data and the new data. What effect, if any, does subtracting 0.5 from every observation have on the sample variance? What percentage of the measurements will lie within three standard deviations of the overall mean? Does the result agree with Tchebysheff's Theorem? Find the percentage of measurements in the intervals plusminus s and plusminus 2s. Compare these results with the Empirical Rule percentages, and comment on the shape of the distribution. In how many provinces is the average gas price stabilized?Explanation / Answer
SOLUTION:-
a)
mean =(95.863+97.902+101.144+103.379+103.621+105.720+106.006+109.722+114.246)/9
= 93.22
list of deviations = {2.616,4.682,7.924,10.159,10.401,12.5,12.786,16.502,21.026}
squares ={6.843,21.921,62.789,103.205,108.180,156.25,163.481,272.316,442.092}
sum = 1337.0776
standard deviation =1337.0776 = 36.566
variance = 28.5002477778
b) Range = 114.226-95.863 = 18.363
Range is half the standard deviation
c)
range = 0.5 x standard deviation (approx, only in this case)
d) new set ={ 95.363,97.402,100.744,102.879,103.121,105.220,105.506,109.222,113.746}
mean=103.68922
variance = 31.9879
variance is increased !
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