the platium gasaver national f
the platium gasaver national fuelsaver corporation naufacturesthe platinum gasaver, a device they claim “may increase gas mileageby 22%” in an advertisment published in the des moines register,the gas mileages with and without the device were presented for 15″identical” 5- liter vehicles. the percent changes in gas mileagefor the vehicles were calculated and are presented here:
48.3 46.9 43.8 44.6 40.2 38.5 34.6 33.7
28.7 28.7 24.8 10.8 10.4 6.9 -12.4
The 12.4% decrease is gas mileage is an outlier in this dataset
(a) find the mean x(with line over it) and the standarddeviation s.
(b) find x(with line over it) and s for the 14 observations thatremain when you ignore the outlier. How does the outlier affect thevaules of x(with libe of it) and s?
(c) what do you think the advertisement means when it callsthese vehicles “identical”
BOOK: THE PRACTICE OF BUSINESS STATISTICS USING DATA FORDECISONS
MOORE, McCABE, DUCKWORTH, ALWAN
SECOND EDITON
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Answer:
a ) let’s use excel for calculation
First enter the given dataset in the excel column.
Then click on Data >ata Analysis >>> DescriptiveStatistics >>>OK
Then select the range of the dataset
Look the following image:
Then click on OK, so we get the following output:
from the above output, we get
= 28.566667
s = 17.5642
Let’s find outliers.
If the value of the given dataset outside ( – 2*s , + 2*s ) this interval then we say that it is outliers.
( – 2*s , + 2*s ) = ( 28.566667 – 2*17.5642 , 28.566667 +2*17.5642) = (-6.56173 , 63.69507)
Only one data value is outside this interval as -12.4
So that -12.4 is an outlier.
b) Let’s find mean and standard deviation after deleting-12.4
Look the following output
Note that -12.4 is smallest value among the given values.
So that the mean obtained from the 14 values after removingsmallest one is increases.
Also when we remove outlier then the variability in the datasetdecrease.
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