# Interpreting Tables of Scientific Data: Practice Problems

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• 0:05 Solving Problems with…
• 0:52 Three Rules for Table Problems
• 4:33 Same Rules, Harder Problem
• 9:18 Lesson Summary

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Lesson Transcript
Instructor: April Koch

April teaches high school science and holds a master's degree in education.

Complex table problems getting you down? Multi-question, situational problems don't have to be a drag on your testing performance. Learn how to apply three simple rules as we walk through two table problems together.

## Solving Problems with Data Tables

Taking a timed science exam doesn't have to be stressful. Usually, if you pace yourself and save the most difficult questions for the end, you won't have to worry about finishing on time. But, one problem that trips up test-taking students is the multi-question problem involving a data table. These problems give you a scientific scenario and a table that sums up the relevant data. You're required to use and interpret the table to answer a series of questions.

This whole process takes a bit of time. It can be unnerving to adjust to a longer problem like this, especially if you've gotten into the groove of taking your test one question at a time. Fortunately, you can learn a few simple rules that will help you streamline your process. Let's take a look at two test examples and learn how to get through these pesky table problems.

## Three Rules for Table Problems

First, we'll check out a two-question problem involving a two-column table. It reads:

The following table contains data for a person's change in exhaled carbon dioxide in response to an increase in respiratory (breathing) rate. Use the table to answer the questions below.

The best thing to do with a problem like this is to scan the table first before you read any of the questions. Many students make the mistake of jumping right into the questions before they understand the table. It doesn't take very long to read the column headings and get oriented to the information.

Our first column shows the respiratory rates measured in breaths per minute. From top to bottom, the breathing rates gradually increase. The second column lists the concentration of carbon dioxide in exhaled air, measured in millimeters of mercury. It looks like the concentrations gradually decrease. So, already we can tell that as breathing rate increases, exhaled carbon dioxide decreases. Maybe we'll be asked about that in this problem; maybe we won't. But, at least now we know what this table is about.

Let's ask ourselves one more thing before starting: Does the table make sense with what we know about biology? In other words, would we expect exhaled carbon dioxide to decrease as breathing rate increases? It's always a good idea to verify the concepts that are referenced in a table problem. You'll want to identify the area of biology that this problem deals with.

We know that carbon dioxide and oxygen are exchanged through the alveoli in our lungs. Blood carries carbon dioxide to the alveoli, where it diffuses through the membrane and into our lungs. That's where our exhaled carbon dioxide comes from! If we increased our breathing rate, there would be less time for gas exchange to occur. We'd gain less oxygen from every breath, and we'd lose less carbon dioxide from our blood. So, it turns out this table does make sense. We would expect exhaled carbon dioxide to decrease as breathing speeds up. Now, let's move on to our first question.

1. What is the relationship between respiratory rate and carbon dioxide concentration?
a. Inversely proportional
b. Directly proportional
c. No relationship
d. Exponentially proportional
e. Logarithmically proportional

Nice - did you hear that? It's asking us something we've already figured out! We said that breathing rate increases while carbon dioxide decreases. But, look at the options we're given in the answers. They're all worded in terms of proportionality and relationships. We can rule out option C because we know that there is a relationship. We can rule out D and E because we can see from the table that there aren't any wildly growing numbers that would indicate a logarithmic or exponential relationship. So, is the relationship between breathing rates and carbon dioxide directly proportional or inversely proportional? In a direct relationship, both variables increase or decrease together. In an inverse relationship, one variable increases while the other decreases. That's the type of relationship we have, so that means A is our answer.

The second question in this problem asks us to identify the line graph that accurately represents the data in the table. We're given four different choices. Now, instead of wasting our time with each little graph, we're going to try and answer the question for ourselves. For most multiple choice questions, you should try to answer the question on your own. This will encourage you to think critically, make you more confident of the answer, and save you from getting tripped up by other options.

If we look at the table and imagine that we're plotting the points on a line graph, we'd end up getting a line that goes down as it moves to the right - a negative slope. You can do a rough sketch of this graph on your scratch paper if you're having trouble during a test. Now, we didn't get a perfectly straight line, so it doesn't match perfectly with any of our choices. But it's pretty obvious which one most accurately represents our data. So, that's our answer.

## Same Rules, Harder Problem

Now let's try a more challenging table problem:

The following image depicts four lengths of sealed dialysis tubing submerged in a solution of 5% sucrose. Each dialysis bag contains a different concentration of sucrose inside. The bags were weighed before submersion, then weighed again every 15 minutes. Use the data in the table below to answer the following questions.

Whoa. This looks like a tough table problem! But remember - don't look at the questions right now. Rule number one is to scan the table first. We're also going to look at the picture they gave us. It shows four different bags in four different beakers. The sucrose concentration is the same inside all the beakers, but we don't know what the concentrations are inside the dialysis bags. The table here will give us a clue.

In the first column, we see time in 15-minute intervals over the course of an hour. Then, we see the weights of each of the dialysis bags over time. Column C really stands out to me because its weight didn't change at all. It looks like bag B got heavier over time and both bags A and D got lighter. So, I know what's recorded in the table. But how does any of it relate to biology?

This is where we need to verify the concepts. Think about the dialysis bags and why their weights are changing. The bags are sealed, so the only way they're gaining or losing weight is for water to diffuse in or out of the bag. Diffusion of water, we know, is called osmosis, and osmosis occurs across a semi-permeable membrane. If you didn't know before, you can easily figure out that dialysis tubing is semi-permeable. Remember, water diffuses through membranes when the solute concentration on one side is higher than the other.

This question must be about osmosis between solutions of different solute concentrations. The dialysis tubing separates two solutions: one in which the solute concentration is 5% and one in which the solute concentration is unknown. We can only guess what the concentrations are inside the bags based on whether they gain or lose water through osmosis. That's what the table's for, and that's what they'll probably ask us about.

Okay, first question:

1. What accounts for the change in weight for bags A, B, and D?
a. Addition of water to the beaker
b. Subtraction of water from the beaker
c. Diffusion of water through the dialysis tubing
d. Evaporation of water from the dialysis tubing

Don't forget to answer the question on your own! We already said the weight change is due to diffusion of water in and out of the bag. So, now we can look at our choices and pick the one that fits our idea.

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