Question 1011301: A civil engineer monitors water quality by measuring the
amount of suspended solids in a sample of river water
over 11 weeks the following observations were
recorded 14,12,21,28, 30, 63,29, 63, 55, 19, 20
Suspended solids (parts per million)
(i) Find the quartiles
(ii) Find the minimum, maximum, range and inter quartile
range,
(iii) Construct a box plot
Answer by mathmate(429)   (Show Source):
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Question:
A civil engineer monitors water quality by measuring the
amount of suspended solids in a sample of river water
over 11 weeks the following observations were
recorded 14,12,21,28, 30, 63,29, 63, 55, 19, 20
Suspended solids (parts per million)
(i) Find the quartiles
(ii) Find the minimum, maximum, range and inter quartile
range,
(iii) Construct a box plot
Solution:
First step is to find out
number of observations=11
and the sorted list in ascending order:
12 14 19 20 21 28 29 30 55 63 63
(i) Quartiles are chosen such that there is an equal number of observation less than or greater than the number. The 3 quartiles are shown below enclosed in vertical bars.
12 14 |19| 20 21 |28| 29 30 |55| 63 63
Therefore the first quartile is 19, second quartile (median) is 28 and third quartile is 55.
(ii)
minimum is 12
maximum is 63
range = 63-12=51
and the inter-quartile range (IQR) = 55-19 = 36
(iii)
see figure below.
The box-plot could also be plotted horizontally.
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