Pad 11:27 AM webassign.net 10.40.142 points Il owskylntroStat1 12.HW 089 A surve

Question

Pad 11:27 AM webassign.net 10.40.142 points Il owskylntroStat1 12.HW 089 A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following boa the results BMW 3 senes BMW 5 series BMW 7 series 25 30 35 40 45 50 55 60 65 70 75 80 Part (a) implies about the distnbution of the data collected for that car seri so the age In complete sentences, describe what the shape of each box plot Each box plot is spread out more in theSelect. values Each plot is skewed to theSelect of buyers are | Select nable than the ages of the lower 50% Part (b) Which group is most lkely to have an outlier? Explain how you determined that The Select- s most likelytohave an outir it has the I-seed-. Part (c) Compare the three box plots what do they imply about the age of purchasing a BMW from he sees when compared oech while older people tend to buy the Comparing the median ages, younger people tend to by the -Select This is not a rule, because there is so muchSelect-in each data set Part (d) Look at the BMW 5 series. Which quarter has the smallest spread of data?

Explanation / Answer

BY THE INFORMATION GIVEN IN QUESTION

THE BUYER OF BMW 3SERIES = 130 PEOPLE

THE BUYER OF THE BMW 5 SERIES = 130 PEOPLE

THE BUYER OF THE BMW 7 SERIES = 130 PEOPLE

THEN  

BY THE BOX PLOT

(A) EACH BOX PLOT IS SPREAD OUT MORE IN THE FIRST BOX PLOT VALUES . EACH PLOT IS SKEWED TO THE POSTIVELY SKEWED . SO THE AGES OF THE BUYERS ARE HIGHLY VARIABLE THAN THE AGE OF THE LOWER 50%.

THE ALL BOXES ARE POSITIVELY SKEWED BECAUSE THE LONGER PORTION OF EACH BOX IS IN THE RIGHT SIDE OF THE MEDIAN. AND LOWER PORTION IS IIN THE LEFT SIDE OF THE MEDIAN.

(b) THE OUTLIERS ARE COUNTED BY THE

IQR = Q3-Q1

FOR BMW 3 SERIES IQR = 42 - 29 = 13

h= 1.5 IQR

h= 1.5*(13) = 19.5

upper fence = h+Q1 = 19.5+42 = 61.5

LOWER FENCE = h+Q3 = 19.5+29 = 48.5

THEN OUTLIWER OF BMW 3 SERIES = (68-61.5)+(48.5-25)

= 92.115

FOR BMW 5 SERES

IQR = 55-40 = 15

h= 1.5(15) = 22.5

UPPER FENCE = h+Q3

= 22.5+55 =77.5

LOWER FENCE = h+Q1

= 22.5+40 = 62.5

THE OUTLIER = (77.5-65)+(62.5-32)

= 43

FOR BMW 7 SERIES

IQR=67.5-35= 32.5

h= 1.5(32.5)

= 48.75

LOWER FENCE = 48.75+35 = 83.75

UPPER FENCE = 67.5+48.75= 116.25

THEN OUTLIERS = (116.25-67.5)+(83.75-35)

= 97.5

SO THE OUTLIER IS MORE FOR THE BMW 7 series

THE BMW 7 SERIES IS LIKELY TO HAVE MOST OUTLIERS .IT HAS THE HIGHER VALUE OF OUTLIER.

(C) COMPARING THE MEDIAN AGES YOUNGER PEOPLE TEND TO BY THE BMW 3 SERIES . WHILE OLDER PEOLE TEND TO BY THE BMW 7 SERIES .THIS IS NOT THE RULE BECAUSE THERE IS MUCH

QURTILE DIFFERENCE IN EACH DATA SET.

(D) LOOK AT THE BMW 5 SERIES

FIRST QUARTER

AND THE VALUE OF THE SPREAD = (42-35)

= 7

  

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