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234 Part IV: Quality Assurance
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Solution:
First we arrange the data in ascending order and rank them from 1 to 15 (n = 15)
Data values: 75, 79, 80, 85, 88, 89, 95, 96, 97, 99, 104, 105, 110, 115, 140
Ranks: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
We now find the ranks of the quartiles Q 1 , Q 2 , and Q 3 . Thus, we have
Therefore the values of Q 1 , Q 2 , and Q 3 are
Interquartile range is
and
Rank of Q 1 = (25/100)(15 + 1) = 4
Rank of Q 2 = (50/100)(15 + 1) = 8
Rank of Q 3 = (75/100)(15 + 1) = 12.
Q 1 = 85 Q 2 = 96 Q 3 = 105.
IQR = Q 3 – Q 1 = 105 – 85 = 20
(1.5) × IQR = (1.5) × 20 = 30.
Figure 18.22 shows the box plot for the above data.
Figure 18.22 shows that the data includes one outlier. In this case, action should be
taken to reduce the activity that produces a noise level of 140 decibels.
Smallest value within
the inner fence
Largest value within
the inner fence
Part IV.A.4
Mild outlier
D C E F
A D
25
55 75 115 135 165
85
96 105
Figure 18.22 Box plot for the data in Example 18.24.
EXAMPLE 18.25
The following data give the number of persons who take the bus during the off-peakhour
time schedule from Grand Central to Lower Manhattan in New York:
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