The article “Hydrogeochemical Characteristics of Groundwater in a MidWestern Coastal Aquifer System” (S. Jeen, J. Kim, et al., Geosciences Journal, 2001:339348) 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.
2099 
528 
2030 
1350 
1018 
384 
1499 
1265 
375 
424 
789 
810 
522 
513 
488 
200 
315 
486 
257 
557 
260 
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?
Answer :
Step 1 of 11 :
Given measurements of electrical conductivity for 23 water sample.
Then the data is given below.
2099 
522 
528 
513 
2030 
488 
1350 
200 
1018 
315 
384 
486 
1499 
257 
1265 
557 
375 
260 
424 
461 
789 
500 
810 
Our goal is to find.
a). Find the mean.
b). Find the standard deviation.
c). Find the median.
d). Construct dotplot.
e). Find the 10% trimmed mean.
f). Find the first quartile.
g). Find the third quartile.
i). Find the interquartile range.
j). Which of the points, if are any outlier?
k). If a histogram were constructed, would it be skewed to the left,skewed to the right,or
approximately symmetric.?
a).
Consider the data.
2099 
522 
528 
513 
2030 
488 
1350 
200 
1018 
315 
384 
486 
1499 
257 
1265 
557 
375 
260 
424 
461 
789 
500 
810 
Now we have to find the mean
Mean is the sum of the total numbers in the data set and divided by the total number.
Then the formula of the mean is
Therefore mean is
Step 2 of 11 :
b).
Now we have to find the standard deviation.
Then the formula of the standard deviation is
SD =
We know that 744.78 and n=23
Substitute the values.
SD =
SD =
SD =
SD = 545.8739
Therefore the standard deviation is 545.8739.
Step 3 of 11 :
c).
First we have to arrange the data smallest to highest.
200,215,257,260,315,375,384,424,...,2030,2099
Then we take the middle value in the data set.
Median is 513
Therefore in the data set median is 513.