The article “Hydrogeochemical Characteristics of Groundwater in a Mid-Western Coastal Aquifer System” presents measurements of various properties of shallow groundwater in a certain aquifer system in Korea. Following are measurements of electrical conductivity (in microsiemens per centimeter) for 23 water samples.
461 500
a. Find the mean.
b. Find the standard deviation.
c. Find the median.
d. Construct a dotplot.
e. Find the 10% trimmed mean.
f. Find the first quartile.
g. Find the third quartile.
h. Find the interquartile range.
i. Construct a boxplot.
j. Which of the points, if any, are outliers?
k. If a histogram were constructed, would it be skewed to the left, skewed to the right, or approximately symmetric?
(a) The mean is
(b) The variance is
The standard deviation is s = 
= 549.84
(c) The 23 values, arranged in increasing order, are:
200, 215, 257, 260, 375, 384, 424, 461, 486, 488, 500, 513, 522, 528, 557, 789,
810, 1018, 1265, 1350, 1499, 2030, 2099
The median is the 12th value, which is 513.
(d)
(e) Since (0.1)(23) ? 2, the 10% trimmed mean is computed by deleting the two highest and two lowest values, and averaging the rest.
The 10% trimmed mean is
(f) 0.25(24) = 6. Therefore, when the numbers are arranged in increasing order, the first quartile is the number in position 6, which is 384.
(g) 0.75(24) = 18. Therefore, when the numbers are arranged in increasing order, the third quartile is the number in position 18, which is 1018.
(h) IQR = 3rd quartile – 1st quartile = 1018 – 384 = 634.
(i)
(j) The points 2030 and 2099 are outliers.
(k) skewed to the right
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