EPPL 612 – Bitto & Goff
Ooo R U, A? ____________________
Salty Seas
Lab Activity: Five Different Methods for Estimating Salinity
Nothing impacts life in an estuary so much as the ever-shifting salinity of the water.
Salinity is the concentration of dissolved ions in the water, especially Sodium (Na+) and
Chloride (Cl-) from the ionic compound NaCl (table salt), but also other ions like
potassium (K+), Calcium (Ca2+), Magnesium (Mg2+), and Sulfate (SO42-). Salinity is
usually measured in parts per thousand (ppt), which is just the percent salt multiplied
by ten. Quite a few methods exist for estimating the total salinity of seawater.
Your Mission: Estimate the salinity of a sample of seawater using five
different methods - hydrometer, refractometer, titration,
evaporation, and conductivity - and evaluate the
accuracy and handiness of each.
Procedure
Your teacher will create a single solution of seawater of unknown salinity. Travel with
your partner(s) to each of the five salinity stations around the room, and make five
independent estimates of the sample’s salinity. Find instructions for each method on the
colored sheets at each station. It doesn’t matter what order you go in. When you finish
a station, just hit the next one available. Record your own estimates of the salinity in the
first row of the Data Table below. Later you will record the estimates made by your
classmates.
Titration
Your
Estimates
Classmate
Estimates #1
Classmate
Estimates #2
Classmate
Estimates #3
Classmate
Estimates #4
Classmate
Estimates #5
Classmate
Estimates #6
Classmate
Estimates #7
Evaporation
Hydrometer
Refractometer
Conductivity
EPPL 612
Epistemology – How Do We Kow What We Know?
Bitto & Goff
Analysis & Interpretation: Descriptive Statistics
Whenever you collect a set of numerical data, you will want to “describe” them
quantitatively using a handful of standard mathematical “statistics.” Descriptive
Statistics fall into two categories: (1) Measures of Central Tendency and (2)
Measures of Dispersion. Some of these, like the “mean” and “range” will already
be familiar to you. Others may not. Descriptive Statistics can provide powerful
insight into the meaning of empirical data, and in this class we will employ them
quite often. In what follows, please take time not only to do the calculations, but
to understand them. The better you grasp these now, the happier you’ll be
down the road …PROMISE!!!
Measures of Central Tendency
Usually when you take samples from a population and collect numerical data, you will
find that most of the values are clustered near the middle of the overall range. Measures
of Central Tendency describe this “middleness” in the data. The most important
measure of central tendency is the Mean, or average. The mean is simply the SUM of
all the data values, divided by the SAMPLE SIZE (n). In the box below, calculate the
mean salinity estimate by the Titration Method for the entire class. Show your work
(yes, I know you can do it all on a calculator, but humor me here and write it all out just
this once!). Round off to the first decimal place.
Another common (though less useful) measure of central tendency is the Median. This
is the CENTERMOST value in your range of data, with an equal number of
measurements above and below it. For the entire class, what is the median salinity by
the Titration Method (if you have an even number of measurements, find the middle two
values and split the difference)? Often, but not always, the median and the mean are
nearly identical. Are they in this case?
One final measure of central tendency is the Mode. This is the MOST COMMON value
in the data set. If you round all the estimates off to the nearest whole number, what is
the modal salinity by the Titration Method?
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Epistemology – How Do We Kow What We Know?
EPPL 612
Bitto & Goff
Measures of Dispersion
To “disperse” something is to spread it out. Measures of Dispersion reflect the “spreadout-ness” in a set of data. They reflect the how widely the actual data values are spread
around the mean, median, and mode. Put differently, they reflect the variability or
“noise” in the data. The simplest Measure of Dispersion is the Range, which is just the
maximum value minus the minimum. What is the range of class salinity estimates by the
Titration Method?
Another important Measure of Dispersion is the Variance, which reflects how “spread
out” the data is around the mean. It’s a bit trickier to calculate, but hey, give it a whirl!
…here’s how:
a) For the Titration Method, write down all your raw values in the first column of
the table below. Then in the second column record the mean over and over
again.
b) Now subtract each of the raw values from the mean. Do this in column #3.
Thus you will have a handful of new numbers, each reflecting a certain
distance, or deviation, from the average.
c) Next, to give us a sense of the spread-out-ness of the data around the mean,
we’d like to sum up all those deviations. But there’s a problem: the sum of
the deviations is simply going to add up to zero, because all the negative
deviations are going to cancel out all the positive deviations! So to get rid of
those negative numbers, simply square all the deviations. Now you have a
new set of numbers, all positive, called squared deviations. List the
squared deviations in column #4.
d) Now add them up to get the sum of squares (next to last cell).
e) Finally, as when you calculated the average, you want to divide by the
sample size. But there’s a small catch, here. When figuring the variance,
you actually divide by the sample size minus one. For example, if the class
made 8 salinity estimates with the Titration Method, divide by 7 instead of 8
(Why??? …don’t ask! It’s a li’l rule you can learn about someday in Stats
class…). This, at last, is your Variance.
Salinity Estimates by Titration
Raw Data
Mean
Deviation from the Mean
Sum of Squares 
Variance 
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Squared Deviations
EPPL 612
Epistemology – How Do We Kow What We Know?
Bitto & Goff
Notice that the Variance reflects how “spread out”
your data is above and below the mean. It
reflects how much the data values “deviate” from
the mean. However, to get rid of all the negatives,
we had to square those deviations.
That
transformed our salinity units from parts-perthousand to parts-per-thousand-squared! Usually,
now, a scientist will “reverse” this act of squaring by
taking the square root of the final variance. The
result is called the Standard Deviation, another
common Measure of Dispersion. What is the
standard deviation of the class salinity estimates by
Titration? Use a calculator, but show your work.
Now calculate (by hand or by calculator) all the Descriptive Statistics for the class salinity
estimates by the Evaporation Method. No shortcuts! Do the math step by step!
Scribble down your work in the big empty space below.
Mean: ______________
Range: ______________
Median: ______________
Variance: ______________
Mode: ______________
Standard Deviation: ______________
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Epistemology – How Do We Kow What We Know?
EPPL 612
Bitto & Goff
Of course, there’s a much easier way to calculate Descriptive Statistics …just let
Microsoft Excel or some other computer program do the math for you! Mean
(“AVERAGE”), Variance (“VAR”), and Standard Deviation (“STDEV”) are all standard
functions in Excel. Go get on a computer, load up Excel, and use it to help you quickly
fill in the table below (you’ve already done the first two columns). Instructions below.
Titration
Evaporation
Hydrometer
Refractometer
Conductivity
Mean
Median
Mode
Range
Variance
Standard
Deviation
How to get Excel to do your Descriptive Stats for you:
For each salinity method, enter raw data down any column. Now click on any
empty cell, then type the “=” sign. Select the function that you want (AVERAGE,
VAR, or STDEV) from the drop-down box to the left of the formula window
upstairs. If you don’t see the one you want, go to More Functions… All…
(Alternatively, you can hit the fx icon beside the formula window; a list of “Most
Recently Used” functions will appear; if the one you seek is not there, hit the
dropdown arrow and select “All”)
Excel will now ask you to specify the range of cells containing the raw data. To
select these cells manually, first click the red, white, & blue icon to the right. This
frees you to go back to the spreadsheet and manually select the data cells by
clicking and dragging. Enter. Enter. Et voilà!!! C’est tout!!!
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EPPL 612
Epistemology – How Do We Kow What We Know?
Bitto & Goff
Analysis & Interpretation Part Two: Evaluation of the Methods
Have a good look at all your and your classmates estimates of the salinity. What’s the
true salinity of our seawater sample? (this is a trick question)
Even though everyone in class was working with the same sample of seawater and
using the same five methods for estimating salinity, no single Salinity emerges. Offer
several possible explanations for this dispersion (“noise”) in the data.
Precision refers to the consistency of results yielded by a method of measurement. The
less “noisy” the results, the more “precise” it is. Which method seemed to yield the most
“noisy” data? Which method yielded the least noisy data? Justify your answers with
descriptive statistics.
Accuracy is how close one’s estimate of something comes to the “true” value. Which
method do you think renders the most “accurate” estimates? Based on what?
…but is it possible to know for sure which method is most accurate??? Why or why not?
Is it possible for a method to be highly precise yet inaccurate???!!! Explain.
Which method(s) is most convenient? Which is most cumbersome?
On a rocking boat, which methods would be most difficult to employ? Why?
Overall, in terms of accuracy, precision, and convenience, which method do you think is
best for estimating salinity in the field. Defend your position.
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