Making sense of tables

46025_mini.jpg (11249 bytes)
In this section, I'm going to review a few basics about tables. As with maps, the goal here is to help you understand the various ways that information are represented. Maps and table and graphs present information in a visual manner that organizes it and lets us see more clearly what's going on. These forms of visual information impact just about everything we do: they inform us about the weather or sports, they help us buy a car or house, they help us prepare marketing and other types of business information, they help fishermen and sailors avoid storms, they might even help a hairdresser choose the right color of tint for your hair.

Visual information plays a big part in our everyday lives so it behooves all of us to know how to make sense of them.

Table and graphs are the easiest way to display numerical information, such as the number of fish in each ocean, the percentage of surfers that are men, women or children,  the temperature of the ocean from San Diego to San Francisco or wave heights in the North Pacific ocean

They make it easier for us to see trends in numbers. Trends is a word we hear a lot, especially in the media: "discover the latest trends in men's swimwear" or "the southland has been experiencing a warming trend" or "that girl is sooo trendy." It's also a word we will use a lot in this class so it's best you know what it means.

Main Entry: 1trend
Pronunciation: 'trend
Function: intransitive verb
Etymology: Middle English, to turn, revolve, from Old English trendan; akin to Middle High German trendel disk, spinning top
Date: 1598
1 a : to extend in a general direction : follow a general course <mountain ranges trending north and south> b : to veer in a new direction : BEND <coastline that trends westward>
2 a : to show a tendency : INCLINE <prices trending upward> b : to become deflected : SHIFT <opinions trending toward conservatism>

The difference between a table and a graph is the way in which the numbers, called data, are displayed. (Just so you know here and now, the word "data" is plural. For example, the data are complete, not the data is complete.) Tables provide rows and columns of data and graphs provide a visual picture of the data in the form of an x-y plot, a bar chart, a pie chart, a column chart, a stacked column chart, a contour plot, etc, etc. The graph above is a contour plots, but that's getting ahead of the story.

Let's study tables first, since that's where scientists usually put their information first before graphing it.

Tables

A table is simply a set of facts or figures organized into columns. Columns extend down the page. The simplest table is a two-column table.  Here's one I made up:

Age:  # of Surfers
under 18 38
18-22 44
23-30 23
31-50 10
>50 5

The column headers, the information displayed in the first row (rows extend across the page) contain the variables (see below). In this table, the first variable (and column) is Age and the second variable (column) is # of Surfers.

You really shouldn't have any trouble interpreting this kind of table and if I asked how many surfers between the ages of 23-30, according to this table, you should be able to give me the correct answer. (If you can't, or you just want to make sure, then e-mail me.) Tables really don't get much more complicated than this. There may be more columns, but they are usually always organized in the same fashion.

The words "variable" often trips up students so let's make sure we understand it:

Main Entry: 2variable
Function: noun
Date: 1816
1 a : a quantity that may assume any one of a set of values b : a symbol representing a variable
2 : something that is variable

Simply put, a variable is something that can change. The age of surfers is a variable, the temperature of the ocean is a variable, the height of the surf is a variable. Try to think of some other variables with which you are familiar.

Variables are commonly represented by a symbol. Now before your mind starts to go numb and your eyes start to glaze over, read these jokes, then return to this page and continue your studies.

A symbol can be anything. The American flag is a symbol. The letters in the words on this page are a symbol. Your name is a symbol. Think about it. A flag can symbolize any country or organization or belief system in the world, depending on its colors and/or the symbols printed on it. The same letters in another language (and even ours!) can symbolize different words or meanings. (Take "wave" for instance; the same letters symbolize a hand movement, energy passing through the ocean or people jumping out of their chairs at a football stadium!). Your name can symbolize any of a multitude of other people. It doesn't mean you are all the same person, just that you have the same symbol. And symbols represent variables!

I emphasize this because so many of us struggle with the abstract concept of symbols. When I write A+B=C or X+Y=Z on the chalkboard, there is a noticeable stiffening in the room; students get nervous! If I put 5+2=7 or 8+9=17, they relax. But if I ask them this question: if A=5 and B=2, what is C? or if X=8 and Y=9, what is Z? they are stunned like a deer in headlights. No kidding! If you're one of those people, then join the crowd. I am one of those people.

In the equations above, I could have used any letter or any other symbol to represent the variables. I could have written the equation like this:

A_5bdolph.gif (17449 bytes) + salmon.gif (21532 bytes)= trsmturtlem.gif (19967 bytes)

And I could have asked:

If  A_5bdolph.gif (17449 bytes)= 5

and

if salmon.gif (21532 bytes)= 2

then how much is: trsmturtlem.gif (19967 bytes)?

It sure would make math more interesting if we used dolphins and salmon and turtles instead of As, Bs, Cs, Xs, Y,s and Zs. But the point is that the result would be no different. The symbols represent variables. Got that?

So much of what we do in this course (and in our daily lives) requires that we use symbols and that we use these symbols to represent variables. We will see some simple wave equations later on (that will allow us all to become surf forecasters) and we will need to understand how to plug-in the numbers. There's really no getting around it. So take the time now and make sure you understand what variables are.

Let's look at a slightly larger table from the web site for SurferGirl Magazine:

logo_sg4.gif (1195 bytes)

1999 "WCT" Ratings As Of July 11, 1999 (Billabong/Mitchell Surfing Foundation Pro, South Africa)

Place

Surfer

From

Points

1999 $

Career $

1

Beachley, Layne

Aus

4360

n/a

$267,685

2

Brooke, Serena

Aus

3510

n/a

$120,445

3

Redman, Melanie

Aus

3040

n/a

$81,015

4

Abubo, Megan

Haw

n/a

n/a

$63,325

5

Falconer, Neridah

Aus

n/a

n/a

$209,160

6

Todd, Trudy

Aus

n/a

n/a

$134,795

7

Tavares, Maria Tita

Brz

n/a

n/a

$40,850

8

MacKenzie, Lynette

Aus

n/a

n/a

$169,015

9

Rogencamp, Yvonne

Aus

n/a

n/a

$23,240

10

Ballard, Rochelle

Haw

n/a

n/a

$163,515

11

Dryden, Sandie

Aus

n/a

n/a

$37,535

12

Menczer, Pauline

Aus

n/a

n/a

$294,705

13

Jeffries, Prue

Aus

n/a

n/a

$66,890

14

Silva, Jaqueline

Brz

n/a

n/a

$21,650

15

Tasker, Hayley

Aus

n/a

n/a

$23,640

How many columns are in this table? What are the variables in this table? Write them down then click here for to check your answers.

Note the entry n/a in the table above. N/A stands for not available, meaning there are no data for that variable.

Note that each instance of data in a table has its own unique cell. A cell is simply a "placeholder" so to speak; you might think of it as the square of space in which a single data entry appears. Each cell belongs to a unique column and row combination. For example, find the first entry of n/a above. Trace it back to its row number and column number. You should be able to see that the first entry of n/a in the table above occurs in the second row (row 2) and the fifth column (column 5). The cell number for this entry would be written, therefore, as R2C5 or C5R2, depending on the convention adopted.

Your understanding of tables and rows and columns and cells will increase significantly if you take a few moments to look at any common spreadsheet software. You don't need to know how to use it. Just open up a new page and look at it. Good spreadsheet programs label (there's that word again) the rows and columns to make it easy to identify any particular data entry. And just so you know, a data entry is often called a data point.

Are you still with me? I hope so.

Here's one more table that starts to get a little closer to the kinds of things we'll be looking at this semester. This table comes from a weather buoy permanently moored in the waters near Catalina Island. The buoy is maintained by the National Data Buoy Center.

National Data Buoy Center: Station 46025 - Catalina RDG - 1999
MM DD HH WDIR WSPD GST WVHT DPD APD MWD PRES ATMP WTMP DEWP VIS PTDY
Z kts kts ft sec sec in F F F mi mb
07 17 00 W 7.8 9.7 4.3 11 9.1 - 29.94 63.1 65.8 57.0 - -1.0
07 16 23 W 7.8 9.7 4.3 13 9.4 - 29.95 63.0 65.8 56.5 - -0.8
07 16 22 W 7.8 9.7 3.6 11 8.7 - 29.97 62.2 65.8 56.3 - -0.8
07 16 21 WSW 7.8 7.8 3.6 13 8.3 - 29.97 62.2 65.8 56.7 - -0.7
07 16 20 WSW 7.8 9.7 3.9 13 8.7 - 29.97 62.2 65.8 56.8 - -0.6
07 16 19 SW 5.8 5.8 3.6 13 7.9 - 29.99 63.0 65.1 57.0 - +0.0
07 16 18 SSW 5.8 5.8 3.6 13 8.2 - 29.99 63.1 64.9 57.2 - +0.7
07 16 17 SSW 1.9 5.8 3.6 17 7.9 - 29.99 63.5 64.4 57.4 - +0.9
07 16 16 S 3.9 5.8 3.6 13 8.0 - 29.99 62.2 63.7 55.9 - +1.3
07 16 15 SSW 1.9 3.9 3.6 14 8.3 - 29.97 62.1 63.5 55.9 - +0.8
07 16 14 S 1.9 3.9 3.9 14 8.3 - 29.96 61.5 63.5 55.9 - +0.6
07 16 13 S 1.9 3.9 3.6 14 8.1 - 29.95 61.5 63.5 56.8 - +0.0

Not counting the columns that are blank (which are used as spaces to make the table easier to read), how many variables are represented in this table? Make a list of them and click here for to check your answers.

Now, to really make sure you understand how to read a table, answer the following questions:

  1. What is the water temperature at midnight on July 17?
  2. What is the air temperature at 5 pm (1700) on July 16?
  3. What date and time is it in California when the atmospheric pressure is 29.96 inches?
  4. Click here to check your answers.

Hopefully, this review has sharpened your ability to find information in a table. We will see lots of different kinds of tables this semester and we'll do a lot more with the data. For now, though, just make sure you are comfortable with how tables are organized. Read through the material one more time and make sure you understand it. If not, you know what to do...post your questions on the forum or send me an e-mail!

A: There are six columns in this table, one for each variable: place, surfer, from, points, 1999$ and career $ are the variables. Place refers to their standings in terms of points; Surfer refers to the name of the surfer; From refers to their country or state of origin; Points refers to the number of points they earned; 1999$ refers to how much money they earned in $1999; and Career$ refers to the amount of money they have earned in their entire surfing career.

B: There are 16 data columns. The variables are mm (month) dd (day), hh (hour, in Zulu time), wdir (wind direction), wspd (wind speed), gst (gusts), wvht (wave height), dpd (dominant period), apd (actual period), mwd (mean wave direction), pres (atmospheric pressure), atmp (air temperature), wtmp (water temperature), dewp (dew points), vis (visibility), and ptdy (pressure trend).

C. 1) At midnight, or 00 hours on July 17, the water temperature is 65.8 degrees F. 2) At 1700 hours on July 16, the air temperature is 63.5 degrees F. 3) On July 16 at 0600 Pacific Standard Time (1400 Zulu), the atmospheric pressure is 29.96 times. Note that the times listed are Zulu times. California is 8 hours earlier than Zulu.