Question 1010183: A store sells 12 different kinds of bathtubs. These data represent the maximum number of liters of water that the bathtubs will hold.
240
272
280
285
295
285
300
290
310
305
285
305
Compute the five-number summary for these data, Be sure to identify all outliers of the data set. Use the values of the upper and lower fences to explain your answer.
(I know the minimun is 240 & the Maximum is 310. the mean is 287.6)
Answer by mathmate(429)   (Show Source):
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Question:
A store sells 12 different kinds of bathtubs. These data represent the maximum number of liters of water that the bathtubs will hold.
240,272,280,285,295,285,300,290,310,305,285,305
Compute the five-number summary for these data, Be sure to identify all outliers of the data set. Use the values of the upper and lower fences to explain your answer.
Solution:
The given values are:
240,272,280,285,295,285,300,290,310,305,285,305
with n=12.
The sorted set of numbers is:
240 272 280 285 285 285 290 295 300 305 305 310
We put a "|" symbol to indicate the locations of the first quartile (Q1), median and third quartile (Q3).
240 272 280 | 285 285 285 | 290 295 300 | 305 305 310
Hence we determine the following statistics:
minimum = 240
Q1 = 282.5
median = 287.5
Q3 = 302.5
maximum = 310
and consequently the five-number summary is (240,282.5,287.5,302.5,310)
The interquartile range (IQR) = Q3-Q1 = 20
We proceed to calculate the lower and upper fences.
Lower fence = Q1-1.5(IQR)=252.5
Upper fence = Q3+1.5(IQR)=332.5
Edited (2015-12-14):
Since 240 falls below the lower fence (252.5), we conclude that 240 is an outlier, hence it should be eliminated from the data and the above calculations repeated.
After eliminating 240, we obtain as sorted list:
272 280 285 285 285 290 295 300 305 305 310
and five-number summary:
272.0 285.0 290.0 302.5 310.0
1.5IQR = (302.5-285) = 26.25
and the fences are:
Lower fence = 285-26.25 = 258.75
Upper fence = 302.5 + 26.25 = 328.75
Since this time around, no data falls outside of the fences
(check: min=272>258.75, max=310<328.75)
We conclude that there are no more outliers in this trimmed list
272 280 285 285 285 290 295 300 305 305 310
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