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Exercises
15.1 Chlorophenol. The sample of n = 20 observations of chlorophenol was reported with the four
values below 50 g/L, shown in brackets, reported as “not detected” (ND).
63 78 89 [32] 77 96 87 67 [28] 80
100 85 [45] 92 74 63 [42] 73 83 87
(a) Estimate the average and variance of the sample by (i) replacing the censored values with
50, (ii) replacing the censored values with 0, (iii) replacing the censored values with half
the detection limit (25) and (iv) by omitting the censored values. Comment on the bias
introduced by these four replacement methods.
(b) Estimate the median and the trimmed mean.
(c) Estimate the population mean and standard deviation by computing the Winsorized mean
and standard deviation.
15.2 Lead in Tap Water. The data below are lead measurements on tap water in an apartment
complex. Of the total n = 140 apartments sampled, 93 had a lead concentration below the
limit of detection of 5 µg/L. Estimate the median lead concentration in the 140 apartments.
Estimate the mean lead concentration.

Pb (µµ µµg// //L) 0–4.9 5.0–9.9 10–14.9 15–19.9 20–29.9 30–39.9 40–49.9 50–59.9 60–69.9 70–79.9
Number 93 26 6 4 7 1 1 1 0 1
15.3 Lead in Drinking Water. The data below are measurements of lead in tap water that were
sampled early in the morning after the tap was allowed to run for one minute. The analytical
limit of detection was 5 µg/L, but the laboratory has reported values that are lower than this.
Do the values below 5 µg/L fit the pattern of the other data? Estimate the median and the
90th percentile concentrations.
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