Key Concept: Averages, Range, and Standard Deviation, with A level Biology Past-Paper Questions

You need to know some maths for A level Biology. This includes knowing how to interpret averages (mean, median and mode), ranges, and standard deviations to work out whether an experiment can be said to have shown an effect or not. Master this early on and it will not help you with exam questions, but also make it easier for you to learn the bits of the course that are explained using these statistical methods.

Why does Biology need so much data?

Maybe the guy at the back is just big for his age?

Researchers often want to compare two or more things. Which species of frog is heavier? Which type of soil grows taller plants? At what temperature do these bacteria divide fastest? At which pH are fish most active?

The biological world is complicated, so multiple, repeated measurements are usually required.

There are three main reasons for taking multiple measurements:

1. Measurement errors. It’s hard to take measurements in the real world. Even if you re-measure the exact same thing, and even if you use a well-calibrated tool, you might get a slightly different result each time. Maybe you can’t hold the tool still enough, or you can’t read it clearly, or the thing you’re measuring moves. These are precision errors.

2. Individual variation. If you want to ask a general question about a whole population, eg “do robins sing more than blackbirds” then you need to measure data from more than two individuals. If you only use two, you might randomly pick outliers; maybe you get a particularly perky robin, or a lazy/sick blackbird. Similarly, if you sample a small area of a larger region, you may not pick a representative area.

3. Uncontrolled variables.There will nearly always be variable-influencing factors that you’re not aware of, or unable to control. Maybe there are changing sounds or smells in the environment, subtle changes in light, or in the birds’ blood-sugar levels. These can affect individual measurements in unpredictable ways.

All of these things can affect the value you record, making any one single measurement unreliable. So researchers normally end up collecting large sets of measurements. In this way they can get a much better idea of what’s really going on.

Why does Biology need Statistical techniques?

Plotting lots of repeated measurements for different datasets on the same graph can create a confusing mess. Also, “the data look different to me” isn’t good enough for science.

Reducing each dataset to just two or three values makes it much easier to compare. In fact, it’s so simple that such data can be understood even without a graph, so values are often presented very simply in a table.

Calculating Averages in Biology

There are three types of average: mean, median, and mode. They all reduce the data set to one single number.

This is useful for comparisons. For example, if you let a frog jump ten times, measuring the length of every jump, you can calculate their average jump length. You can then compare that single number to the average jump length from another frog to find out which jumps further.

Calculating the Mean

The most important type of average for A level Biology is the mean. It’s also what most people are talking about when they say “average” in everyday life.

To find the mean, add up all the numbers, then divide by how many numbers there were. You end up with just one number.

Here’s an example dataset:

How to calculate the mean:
3 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7 + 8 = 55, so the total is 55
There are ten numbers, so n = 10
The mean is the total divided by n, which is 55/10, which is 5.5

Example exam question 1:

What is the missing number?

Find answers to Question 1 at the bottom of this webpage

Calculating the Median (unaffected by outliers)

What if we had the same data as above, but one of the measurements was … strange.

Set 1

3

4

5

5

5

6

6

6

7

8

total = 55   /   n = 10   /   mean = 5.5

Sometimes, datasets include odd numbers. It’s not clear whether the 48 here was an error in measurement, or whether it’s genuine. If it is measuring individual organisms, maybe the outlier is a strange mutant? But either way, outliers like this can do very strange things to the mean value.

How useful is the mean for this dataset?

To avoid the problem of a small number of outliers moving the mean away from where it would otherwise be, you can opt to use a different average, the median.

The median is found by putting the numbers in order of size (as they already are here) and picking the middle one. If there are two middle ones, take the mean of those two.

Here there are ten numbers. The two numbers in the middle are 5 and 6. The mean of these is (5+6)/2 = 5.5

Set 1

3

4

5

5

5

6

6

6

7

48

total = 95   /   n = 10   /   mean = 9.5

By ignoring the strange outlying number(s), we get an average that is more useful than the mean would be.

Example Exam Question 2:
How similar are the mean and median values for this data? (Answers at the end of this blog post.)

(d) Complete the table above to show the median and mean diameters.

Find answers to Question 2 at the bottom of this webpage

Calculating the Mode (the most common value)

There’s one more type of average value you need to know. The mode is just the number that is most frequently found in your dataset. Of course this only makes sense if there are plenty of repeated numbers present in the dataset.

Set 1

3

4

5

5

5

6

6

6

7

48

central number(s) = 5 and 6   /   median = 5.5

The mode is another way to stop outliers affecting your average.

Choosing which type of average to use

You might be asked to choose which average is most appropriate. Can you answer this exam question?

Example Exam Question 3:

Find answers to Question 3 at the bottom of this webpage

Moving Beyond the Average

Why the average isn’t enough

There’s a big problem with just using the average by itself to compare two sets of data. The problem is that very, VERY different sets of data can give you the exact same average value.

Compare these three sets of data:

Set 1

1

3

5

5

5

5

6

6

7

48

mode = 5

Set 1		50	50	50	50	50	50	50	50	50	50		mean = 50   /   median = 50   /   mode = 50
Set 2		25	30	35	40	50	50	60	65	70	75		mean = 50   /   median = 50   /   mode = 50
Set 3		1	2	3	4	50	50	96	97	98	99		mean = 50   /   median = 50   /   mode = 50

The averages are the same! By themselves, averages only tell you one small part of the story.

What is Range / why is it useful

One of the big differences betwen the datasets above is the range of numbers that appear.

The range is the range-of-values that appear, from the lowest to the highest.

Set 1		50	50	50	50	50	50	50	50	50	50		lowest value = 50   /   highest value = 50   /   range = 50 to 50
Set 2		25	30	35	40	45	55	60	65	70	75		lowest value = 25   /   highest value = 75   /   range = 25 to 75
Set 3		1	2	3	4	50	50	96	97	98	99		lowest value = 1   /   highest value = 99   /   range = 1 to 99

Set 1 has a range of 50 to 50. So you can reasonably predict that the next measurement would likely be 50 too
Set 2 and Set 3 have wider ranges. There are a wider range of possible values that might be measured, so it’s harder to predict what the next measurement might be.

A wide range might indicate that your measurement technique is very unprecise, or that there is a wide natural variation in the thing you are measuring, or that there is another factor affecting your measurements.

But a wide range might also just mean there were one and two weird outliers in the data. So you need to be careful when using this value. Here is a set with one odd measurement, which might be due to a measurement error.

Finding the Range

Example Exam Question 4:

The answer is at the bottom of this webpage

Why do we need Standard Deviation

The Standard Deviation tells you how similar the numbers you used to calculate your mean are. Were they very close together in value, or very different?

It’s different from the range because it tells you how closely the measurements were clustered around the mean. This tells you how useful the mean will be when comparing it to the mean from other data sets. It is also not affected by weird outliers in the way that the range is.

These two data sets have the same mean averages (50) and the same range (25-75):

Set 4

50

50

50

50

50

50

50

50

50

90

lowest value = 50   /   highest value = 90   /   range = 50 to 90

Set 1		25	42	48	50	50	50	50	52	58	75		values clustered around mean = low standard deviation
Set 2		25	30	35	40	45	55	60	65	70	75		values spread out away from mean = high standard deviation

To understand Standard Deviation, think about a situation where you have made very many measurements, so that you have multiple measurements at each possible value. Now plot these on a graph (see below). In biology, you usually see that the graph forms a bell shape. This is called a “Normal distribution”.

Normal distributions are symmetrical, so the mean, mode, and median are all the same, appearing at the centre of the graph (mean, median, and mode = 16 in this example). In normal distributions, most measurements are near the average, so there is a peak in the middle of the graph.

(Sometimes, you’ll find a curve is skewed a bit to one side. This separates out the mode, median and mean values. But for our purposes, I’m going to stick to thinking about the symmetrical graph.)

How wide the curve is matters a lot, because it affects how much two sets of data overlap. Compare these two examples below. Both have one set of data where the mean is 14 (plotted in orange), and another set where the mean is 20 (plotted in blue).

There is the same amount of data in both graphs, and the averages haven’t changed. But there is a lot less overlap between the two datasets in the example to the left. The data on the right is a lot more spread out away from the average values.

When datasets overlap a lot, you need to be very careful that you definitely have enough data to be sure their means really are different. If you have a small data set with a lot of variation, then adding extra measurements can make a big difference to the mean.

What is Standard Deviation

Standard Deviation tells you how widely the data is spread out in a normal distribution. Its symbol is sigma, “σ”.

You’re very unlikely to be asked to calculate standard deviation in an exam, and it takes a while to explain so I’m not going to go through it here (don’t worry they’d give you the equation if you did have to do this).

But you do need to know what it tells you.

Here is the basic normal distribution graph again. The graph is symmetrical and the mean (μ) is in the centre.

Now here is the same graph, but two more values are marked on the x-axis, shown by orange lines. These are the value of the mean minus one standard deviation (μ-σ), and the value of the mean plus one standard deviation (μ+σ).

If you colour in the bit of the graph that is within one standard deviation of the mean (from μ-σ to μ+σ), then on any normal distribution, 68.27% of the data points will lie within this area. You don’t need to remember that percentage, but remember it is always the same.

This means that if the standard deviation is a small number, you know most of the data points are close to the mean. This gives you more confidence that the mean is a useful value for comparison.

The graphs below have the same X-axis. Both are normal distributions with the same mean. But the one on the left has a small standard deviation, and the one on the right has a high standard deviation. (Some of the data from the right-hand graph falls outside the values shown on the graph.)

How to tell if there is a significant difference between values using the mean and standard deviation

!! Ok so this is the important bit we’ve been building up to !!

In a normal distribution, most of the data (68.27%) falls within one standard deviation of the mean. This is the area between μ-σ and μ+σ.

To work out whether it’s just chance that the means are different, or whether it’s a real effect, you need to check whether this area overlaps bewteen the two sets of data.

If the areas between μ-σ and μ+σ overlap, the difference is not considered significant.

There are different ways of presenting the data.

Standard Deviations Using Numbers - example

An example:

Set 1: mean (μ) = 50, standard deviation (σ) = 8
Set 2: mean (μ) = 40, standard deviation (σ) = 3

Are these sets of data significantly different? Look at the areas between μ-σ and μ+σ

Set 1: μ-σ = 42 and μ+σ = 58
Set 2: μ-σ = 37 and μ+σ = 43

Do these areas overlap? Yes they do (both include 42-43). So you can not consider the two data sets significantly different.

(Also worth knowing: nearly all the data (95.45%) falls within two standard deviations (between μ-2σ and μ+2σ) - so if these two areas don’t overlap you can be even more sure the two sets of data really are different.)

Standard Deviations Plotted on Graphs - example

On graphs, the mean is plotted as usual, with a dot or column. Extra lines extend out to show the area from μ-σ to μ+σ. This can make it more obvious whether areas overlap or not (unless they are super close in which case numbers are more useful).

Standard Deviation Exam Past Papers

Example Exam Question 5

Question 5 answers found at the bottom of this web page

Understanding Standard Deviations from Graphs

Example Exam Question 6

Question 6 answers found at the bottom of this web page

Example Exam Question 7

Question 7 answers found at the bottom of this web page

Graphs and Tables in A level Biology

If you’re not confident with questions that include graphs and tables, see the recent blog post “How to Approach A level Biology Graph and Table Questions: Tips and Exam Question Pack”, which offers more useful tips for navigating them during exams, and more exam questions to practice with.

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Answers to example exam questions

1. The data for the damaged block should be ignored. The mean for shape C is 3520 seconds

2. Cinnamon Oil median = 16, mean = 17 ….. and ….. Postive Control median = 12, median = 13

3. Median = 41. This avoids the outliers affecting the value as would happen if you used the mean. And the sample size is too small to use the mode (there are no repeated values)

4. The range is 2 to 11

5. Bull terrier genetic diversity is significantly the smallest of the breeds shown, meaning it the most inbred. Jack Russell genetic diversity is significantly the greatest. The genetic diversity of Miniature terrier and Airedale terriers are similar with no significant difference between the two.

6. Standard deviation is spread of data around the mean; using standard deviation reduces effect of anomalies/ outliers; standard deviationcan be used to determine if (the difference in results is) significant/not significant/due to chance /not due to chance

7. Trapping increases enzyme/GOx/HRP activity; the difference/increase is significant (it is unlikely to be due to chance as the standard deviations do not overlap)

Key Concept: Surface Area to Volume ratio (SA:V)

Some concepts turn up again and again in A-level biology. Taking a little time to ensure you really understand these key concepts from the start can save a lot of effort overall.

Surface area to volume ratio (SA:V) is vital for understanding a wide range of topics including transport across cell membranes, gas exchange, digestion, heat exchange, and mass transport. SA:V explains why the inner membrane of a mitochondrion is folded, why elephants have big ears, and why jellyfish don’t need blood vessels.

How confident are you in calculating this value and understanding its significance?

What are surface-area-to-volume ratios?

"Microvilli-Duodenum" by Wbensmith is licensed under CC BY-SA 3.0.

The ratio tells you about how changing the shape or volume of something affects its surface area. It’s not as simple as many people think: doubling the volume of ice-cream in a choc-ice doesn’t double the area of chocolate needed to cover it.

Surface areas are really important in biology. And so the shapes and volumes of things including organelles, cells, and organs are often optimised with respect to surface area. Whenever you see a weirdly folded or worm-shaped structure, think about SA:V.

Surface area to volume ratio (SA:V) is a value calculated by dividing a thing’s surface area by its volume. It is a single number that tells you about the relationship between the two input values.

To be precise: SA:V tells you how much surface area there is per unit of volume.

How to calculate SA:V (it’s not difficult, you just divide)

Quick maths refresher

You will need to think about length, area, and volume and understand their units. Here’s a reminder for cuboids:

Simple example

Imagine a cube where every edge is 1 cm long. (Note: this blog doesn’t let me write little superscript numbers so I’ll use ^ to indicate that the following number should be written superscript, so 1^2 would mean 1-squared.)

1. Each square face of the cube has a surface area of 1 cm x 1 cm = 1 cm^2

2. Cubes have six faces, so the total surface area is 6 x 1 cm^2 = 6 cm^2

3. The volume of the cube is 1 cm x 1 cm x 1 cm = 1 cm^3

4. SA:V = surface area / volume. In this example that’s 6 cm^2 / 1 cm^3 = 6 cm^-1

Notice the funny unit there. You’ve divided cm^2 by cm^3 so they don’t cancel out perfectly.
But does it matter what this unit is? Let’s try it using the same cube but measuring it in millimetres.

1. Each square face of the 1 cm cube has a surface area of 10 mm x 10 mm = 100 mm^2

2. Cubes have six faces, so the total surface area is 6 x 100 mm^2 = 600 mm^2

3. The volume of the cube is 10 mm x 10 mm x 10 mm = 1000 mm^3

4. SA:V = surface area / volume. Using millimetres that’s 600 mm^2 / 1000 mm^3 = 0.6 mm^-1

1 mm is 1/10 of 1 cm and the SA:V calculated in mm is 1/10 that of the value calculated in cm. If you are comparing SA:V values, make sure they have the same unit.

Of course you don’t find a lot of cubes in nature. In exams they might simplify cells or other bodies to be imagined as spheres of a known radius, and give you equations for you to calculate the surface area and volume. And there are much weirder shapes to think about too. But before we get to all that …

How does SA:V change as things increase in scale?

We know the 1 cm cube has a SA:V of 6 cm^-1.

So, what if we get a handful of these 1 cm cubes and stick them together to make a scaled-up cube where every edge is 2 cm long? (See picture). How will the SA:V of this new structure compare? It’s still a cube, after all; it’s just a bit bigger.

2-cm cube:

1. Each square face of the assembled cube has a surface area of 2 cm x 2 cm = 4 cm^2

2. Cubes have six faces, so the total surface area is 6 x 4 cm^2 = 24 cm^2

3. The volume of the assembled cube is 2 cm x 2 cm x 2 cm = 8 cm^3

4. SA:V = surface area / volume. In this example that’s 24 cm^2 / 8 cm^3 = 3 cm^-1

The larger cube’s SA:V is only half that of the unit cube!

SA:V is surface area divided by volume. Higher values of SA:V mean there is more surface area for each unit of volume, and lower values of SA:V mean there is less surface area for each unit of volume.

So our 2 cm cube has less surface area per unit volume than the 1 cm cube did.

The larger cube has a lower SA:V. And if you work out the numbers for an even bigger one, you’ll get an even lower SA:V.

This makes sense. To build the 2 cm cube, you stack eight 1 cm cubes together. By doing this, you bury some of their faces within the structure. You end up with the same volume as eight individual 1-cm cubes, but you have reduced the surface area that is exposed to the outside world.

Also, if you look carefully at the picture, you’ll see that each cube in the assembled structure has half of its faces buried. So there’s only half the surface area per unit volume compared to the single cube. And so it makes sense that the SA:V is half what it was for the single cube.

Each small cube is only showing three of its six faces. So for each 1 cm^3 volume (ie for each small cube) there is 3 cm^2 surface area exposed, giving us an overall SA:V of 3 cm^-1.

Key concept: as size increases, SA:V decreases. This is a good thing to explicitly state in any question about SA:V and size, where the shape stays the same.

Try it: calculate SA:V for a 3 cm x 3 cm cube. What value do you guess you might get? And what is the actual value?

Why size matters

"Zygote" by Nina Sesina is licensed under CC BY-SA 4.0.

Imagine you are a single cell (well, you were once, don’t you remember?).

Your cell membrane is your connection with the outside world. Through it you take in nutrients, water and other necessary things. And you expel your waste through it.

This membrane is your surface; you have as much surface area as you have cell membrane.

Meanwhile, inside the cell membrane you have cytoplasm, organelles, etc. In this region you are busily metabolising molecules. You can measure this region as your volume.

• Question: can you take in enough nutrients, and expel enough waste, to keep up with your metabolism?

• More-important question: if you grow bigger, will this still be true?

Valonia ventricosa aka Sailors eyeball - a single cell that can grow up to 5 cm in diameter. But … how???

As a cell grows larger its SA:V falls. This is just like we saw with scaling up the cubes above. The growth of the cell’s surface area (cell membrane) just can’t keep up with the growth of its volume (where the metabolism is). This means there will be a point at which there just isn’t enough cell membrane (surface area) to transport everything that needs to be transported, limiting the cells ability to function.

This is one reason why cells tend to be pretty small!

But … wait a minute, what about the freakish cell in this next photo? A shiny, bright green, single-celled alga that can get up to 5 cm in diameter. A single cell! Charmingly known as ‘sailors’ eyeballs’.

But how can one cell possibly be so large? Isn’t its SA:V ridiculously low? (Spoiler: yes it is). How can it transport everything it needs with such a low SA:V? Well, it has a trick …

Shape matters

This giant cell is cheating. Inside, all the metabolic activity is limited to an area very close to its cell membrane. Nearly all of the cell’s interior is filled up by one giant vacuole that pushes all the interesting stuff out to the region next to the membrane. So there isn’t nearly as much metabolism going on in there as you might imagine from its total volume. If you re-calculated its SA:V ignoring the volume inside its vacuole, you’d get a much more sensible number. (It also has multiple nuclei spread throughout its cytoplasm.)

In exams, questions are usually about solid spheres or cuboids. We’ve looked at cuboids, so let’s look at spheres.

Spheres

If you have to calculate for spheres, they will give you the equations you need to calculate volume and surface area. So don’t worry about remembering these.

• Volume of a sphere = 4/3 x π x r^3

• Surface area of a sphere = 4 x π x r^2

So, if you have a sphere of radius 1 cm (remember this is just the distance from the centre to the outside, so the whole thing is 2 cm across):

1. The surface area is 4 x π x r^2. If r = 1, r^2 = 1. So the surface area is 4 x 3.14 x 1 = 12.6 cm^2

1. The volume is 4/3 x π x r^3. If r = 1, r^3 = 1. So the volume is 4/3 x 3.14 x 1 = 4.19 cm^3

2. SA:V = surface area / volume. In this example that’s 12.6 cm^2 / 4.19 cm^3 = 3 cm^-1

This is the same SA:V as the 2-cm cube!

That important phrase “as size increases, SA:V decreases”, is talking about increasing the size of something while keeping the same shape overall. Shape is also really important!

Spheres have the lowest possible surface area for their volume. This is one of the reasons that nature likes them. For example, bubbles are spheres because surface tension pulls their surface in to minimise its area.

Stretching out

If a cell needs to grow to large dimensions but also needs to keep a high SA:V, it needs to avoid being a sphere. More-complex shapes will always have higher SA:V.

Consider neurons. You have a single neuron that reaches from your big toe to your spine. A single cell over a metre long! But these neurons are definitely not spheres. They are very skinny.

Question: what happens to SA:V when you make long/thin shapes?

Let’s go back to the 1 cm cubes. The 1 cm cube had a SA:V of 6. And the 2 cm cube had a SA:V of 3.

The 2 cm cube had a volume of 8 cm^3 : it was made out of eight small cubes. Let’s take those eight small cubes and rearrange them into the shape of a flatworm: a rectangular block of 2 cm x 4 cm x 1 cm (see picture above).

1. The upper and lower faces of this shape each have a surface area of 8 cm^2

2. The two long sides of this shape each have a surface area of 4 cm^2

3. The two ends of this shape each have a surface area of 2 cm^2

4. The total surface area is (2 x 8 cm^2) + (2 x 4 cm^2) + (2 x 2 cm^2) = 28 cm^2 (the 2 cm cube had 24 cm^2)

5. The volume of the assembled cube is 2 cm x 4 cm x 1 cm = 8 cm^3 (ok that isn’t a surprise)

6. SA:V = surface area / volume. In this example that’s 28 cm^2 / 8 cm^3 = 3.5 cm^-1 (the 2 cm cube was 3 cm^-1)

Rearranging it from a 2 cm cube to a flatworm of the same volume has increased its SA:V.

Ok so let’s push it even further and turn it into a long worm.

1. The upper and lower faces of this shape each have a surface area of 8 cm^2

2. The two long sides of this shape each have a surface area of 8 cm^2

3. The two ends of this shape each have a surface area of 1 cm^2

4. The total surface area is (2 x 8 cm^2) + (2 x 8 cm^2) + (2 x 1 cm^2) = 34 cm^2

5. The volume of the assembled cube is 1 cm x 8 cm x 1 cm = 8 cm^3 (no surprise)

6. SA:V = surface area / volume. In this example that’s 28 cm^2 / 8 cm^3 = 4.25 cm^-1 (the 2 cm cube was 3 cm^-1)

Your neurons can be really, really long because they’re also skinny, because that means they still have a really high SA:V.

And of course this works for whole animals too. Many small animals lack blood vessels and rely on molecules simply diffusing through their bodies. They need high surface area for transport and they also need every part of their interior to be not-to-far from that surface. This is (one of) the reasons we don’t have truly-giant insects: they are limited by their ability fo transport things to/from the outside world. Sponges and jellyfish also lack blood vessels and rely on diffusion.

Nemotode by Bob Goldstein, UNC Chapel Hill http://bio.unc.edu/people/faculty/goldstein/ Licenced under a Creative Commons Attribution-Share Alike 3.0 Unported licene

Tardigrade by Alexander Klepnev licenced under CC BY-SA 4.0.

Humans, alongside other larger animals, have much lower SA:V and suffer from low diffusion rates. So we need specialised structures to aid exchange and transport.

Maximising SA:V

Structures that are involved in transport and exchange rely upon having very high surface areas of membrane across which transport can take place. To maximise exposed surface area, structures are folded, or shaped into fingers, or branches.

In the human body, you find extremely high SA:V ratio in specialised structures including:

• Gut - the gut wall has microvilli, finger-like structures that extend into the lumen. These increase surface area for absorption of water and nutrients

• Lungs - the lungs have many branches terminating in tiny alveoli offering a very high surface area for gas exchange.

• Capillaries - capillaries have much higher SA:V than arteries or veins. This offers a higher surface area for transporting things between the blood and tissue fluids. It also increases fluid resistance, which is important to keep the blood moving forward.

• Red blood cells have a biconcave shape that increases their SA:V allowing better gas exchange with the blood plasma.

In other organisms, the shapes of structures like leaves, chloroplasts, gills, root hairs, and fungal hyphae, among many other examples, are similarly optimised to maximise surface area to volume ratios.

Folded membranes

You also find folded membranes used as a way to squeeze a load of membrane into a small space. Eg:

• Mitochondria have a highly folded inner membrane that offers more surface area to embed the enzymes and proteins involved in oxidative phosphorylation, so that more ATP can be produced.

• Golgi apparatus and endoplasmic reticulum are similarly folded to maximise their surface area.

Thermoregulation

Who is is feeling cold, and who is feeling hot?

Body surfaces also exchange heat with the environment.

We naturally change our SA:V when we get hot or cold by changing the position of our limbs and body. Which of the people in the image has the highest SA:V? Which person is feeling cold, and which is feeling hot?

Dogs increase their surface area by opening their mouths when hot and panting (passing air over their wet surfaces to lose heat through evaporation). Cats form neat loafs when cold but sprawl dramatically across the floor when hot.

Organisms’ entire body shape will also be related to their thermoregulatory needs.

Animals that need to lose heat from their bodies usually have a higher SA:V, and animals that need to conserve heat usually have a lower SA:V. This is why elephants have such huge ears (more surface area from which to lose heat) and why animals from cold environments tend to be more spherical than those from hot climates.

"Emperor Penguins" by Christopher.Michel is licensed under CC BY 2.0.

"Black Necked Stork" by AntoGros is licensed under CC BY 2.0.

Keep it in mind

If you can get an intuitive feeling for Surface Area to Volume ratios, and keep them in mind whenever you see a question about folded structures, or about similar shapes of different sizes, then this will help you understand what questions are really asking. A level Biology is about the why and how much more than it is about remembering facts, and SA:V goes a long way to help you understand things on this deeper level.

This article was written by Dr Jenny Shipway with guidance from Tom Whitburn

Key Concept: Independent and Dependent Variables

A guest blog from Dr Jenny Shipway, who studied biochemistry at university and now works in science communication and education training.

To understand experimental design and graphs in exam questions, you will need to confidently recognise the difference between different types of variables. Master this now and it will also make it easier to learn content that is taught using graphs.

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What is a Variable

A variable is any value that does/might change during an experiment.

Variables can include things like pH, temperature, colour, or the concentration of substances. The amount of time that has passed is a variable, as are rates of reaction.

• Some variables’ values are fixed deliberately by the scientist.

• Some variables’ values are changed deliberately by the scientist. These changes are planned in advance so the measured values are usually known before the experiment starts.

• Other variables’ values are allowed to change naturally as the experiment progresses. These values can be measured to provide useful data.

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Simplify Your Exam Approach

During exams it’s very easy to get overwhelmed with information. When this happens, your brain makes guesses and jumps, often without you being aware. This is why students so often mis-read graphs and/or make ‘silly’ mistakes.

Excellent Exam Tip: work out what the experiment was and how the graph is presented BEFORE looking at the exam question.

This will …

• Reduce the number of things you’re thinking about at one time

• Reduce the risk of you jumping to (incorrect) conclusions

• Help you focus on understanding the experiment

You might feel an urge to rush forward to look at the question, but trust me that won’t save time. You will not be able to answer the questions unless you understand the graph, and rushing forward will make that more difficult, not less.

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Identifying Variables

Variables described in the experiment and named on the graph axes may include:

• Independent Variable – this is the thing that is changed deliberately by the scientist in a planned way. This is the thing that we expect to cause a measurable effect. 

• Dependent Variable- this is the thing that is measured by the scientist. The value is not known until it is measured, and the value will depend upon the value of the independent variable.

• Control Variables – these variables are fixed to one unchanging value throughout. For example, all experiments might be carried out at 20°C, in which case temperature is a control variable. (Important: this is a different thing from ‘a control’).

The purpose of the experiment is to answer the question: how does the independent variable affect the dependent variable?

There are usually many factors that could be affecting the dependent variable, so it’s important to control as many variables as possile. The idea is that if only one thing has changed (ie the independent variable), then you can be more confident the affect is due to that one thing. 

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An Example 🍅🍅🍅

If you wanted to work out what temperature was best for growing tomatoes, you could try growing plants at different temperatures to see which plant produced the most fruit. Everything except temperature should be kept the same so that you’re sure that any difference in fruit yield is due to temperature.

The question is: how does temperature affect fruit yield?

You will deliberately be changing the temperature to pre-chosen values, so temperature is the independent variable.

You will need to measure the weight of tomatoes produced to find out this value. So this is the dependent variable. The weight of fruit will depend upon the temperature.

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Check your Understanding

Can you identify the independent and dependent variables in the following examples? Which variable was independently fixed by the scientist? And which was measured/recorded during the experiment?

(Ignore the positions of the data points, you only need to look at the axis labels.)

Usually, you will find the independent variable along the x-axis, and the dependent variable up the y-axis. But that’s not always the case (as you hopefully spotted in some of these examples). Do not let your brain jump to an assumption! You must always check this.

You need to be 100% confident of your variables before you move forward to look at the actual question, or everything else will get really confusing. It’s a good tip to write on the exam paper which variable is which (eg label the graph axes “I.V.” and “D.V.”)

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Multiple Independent Variables

It’s possible to have more than one independent variable.

For example, some experiments are run twice under different conditions. See this graph:

First, look at the axes. The independent variable here is the amount of time that has passed (on the x-axis): the scientist decided before the experiment at what times they would count the fruit. The dependent variable is the number of ripe fruit (on the y-axis): the number of ripe fruit is the thing the scientist is measuring, and this depends on how much time has passed when the measurement is taken. We’ve seen this before.

Now look at the data. There are two sets of data plotted on the graph. One experiment has been run with fertiliser, and one without. So the presence of fertiliser is another independent variable – it’s something else that affects the value of the dependent variable.

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Example A-level Exam Questions

Can you identify the independent and dependent variables in the following A level Biology exam questions?

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For more general information about graphs, see the post about how best to approach A level biology graph questions.

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Key Concept: Polar and Charged Molecules

The similarites and differences between non-polar, polar and charged molecules (or parts of molecules) are really important. You must understand the difference between polar and charged molecules if you are going to make sense of molecular structure, and of the ways in which molecules interact.

If you’re unsure if water is a polar molecule or are wondering whether ions are polar, this article is for you.

This molecule is polar, but not charged. All is explained below.

Getting this topic straight in your mind will make it much, much easier to grasp key concepts like why glucose dissolves in water, why other things don’t, and how neurons and mitrochondria use membranes to create ion gradients for their function. And you’ll need to understand hydrogen bonding of polar groups to understand how DNA and proteins adopt defined structures.

The fact the molecules are called ‘polar’ and ‘charged’ is part of the problem - this can be pretty confusing! So don’t rely on their names to understand what’s going on.

Let’s start from scratch:

How are Polar and Charged Molecules different from Non-Polar, Uncharged Molecules?

All molecules contain atoms. And all atoms contain positively-charged nuclei and negatively-charged electrons.

In a non-polar, non-charged molecule, these positive and negative charges all neatly cancel each other out. As far as other nearby molecules are concerned, a non-polar molecule behaves as though it has no charges at all.

In both polar and charged molecules, the molecule has regions of positive and/or negative charges that can affect nearby molecules (or even other parts of the same molecule - as happens in proteins and DNA).

What’s the difference between Polar and Charged Molecules?

Polar molecules are charged-balanced overall but have unevenly distributed electrons. This gives them a little bit of a charge in certain places.

Charged molecules do have an overall charge. They have at leat one full unit of charge on at least one atom. (A unit of charge being equal to the magnitude of one electron).

You will also hear about polar and charged groups, which are a part of a larger molecule, where that part (group of atoms) has these properties.

Now, you might read that and think yes! I’ve got it! But to really understand it - and more importantly to remember it - you are going to need to linger a while and spend a bit of time thinking about this. It’s worth going through it all carefully step by step - this will also check your understanding. Have a good think about where those electrons are. Too many students trip up on this topic.

So let’s look at what it means to be non-polar, polar or charged. And then how that affects the behaviour of these molecules.

First step: What’s the difference between Unpolar and Polar Molecules

Atom

The atoms that make up molecules each have a postively-charged nucleus and a cloud of negatively-charged electrons.

Different types of atoms have different numbers of charges.

This means that even non-charged, non-polar molecules contain charges! They just cancel each other out so you don’t notice them.

Non-polar

When you make a molecule out of atoms, electrons are shared between neighbouring atoms. The electrons become one big shared cloud. This makes a covalent bond.

The diagram shows a non-polar molecule with two atoms. In a non-polar molecule, all the charges are balanced, cancelling each other out.

Because the charges are distributed evenly, and cancel out overall, the molecule behaves as though there are no charges (in terms of its electrostatic interactions with other nearby molecules).

So why are they called “non-polar”? To understand that, you need to understand what polar means.

Polar

It turns out that some types of atomic nuclei just LOVE electrons. Like, they are particularly greedy for them. Oxygen, for example.

These greedy atoms yank the electron cloud over towards their nucleus, away from the nucleus of the other atom.

The other atom no longer has enough negative charge to cancel out its positively-charged nucleus. While the greedy one has more negatively charged electrons than it needs.

The charges no longer cancel each other out. The other atom now has just a little bit of a positive charge, and the greedy one has just a little bit of a negative charge.

This is a polar molecule. Its atoms still share one electron cloud, so they are still covalently bonded. But the small charge in charge distribution mean it will now interact differently with its environment.

Overall, the charges still cancel out. They are just unbalanced so that there are places with just a little bit of charge.

Saying "just a little bit” of charge is a pain, so instead the delta symbol is used to show this.

δ+ = just a little bit of positive charge
δ- = just a little bit of negative charge

This can also happen to just one part of a molecule. A good example is a hydroxyl group (OH). The oxygen pulls the electrons toward it, so that there is just a little bit (δ) of charge on the oxygen and hydrogen atoms.

Molecules with hydroxyl groups are polar. Look at glucose - it has loads of hydroxyl groups; this is what makes it a polar molecule. This is important for how it behaves in water, but before we get to that, let’s look at how charged atoms/molecules are different:

Second step: What’s the Difference between Polar and Charged Molecules?

Polar

A polar molecule has no overall charge. The charge of its positive nuclei exactly cancel out the charge of its negative electrons.

The charges are just unevenly distributed, giving a little bit (δ) of positive charge to one atom, and slight negative charge to another atom.

In biology, you’ll normally find it’s a hydrogen atom that has had its electrons yanked away and is now carrying a little bit of positive charge.

Charged

Now look at this. These atoms are not sharing a cloud of electrons - the big one has gone all-in and taken the whole lot for itself.

No shared electron cloud means there is no covalent bond.

No covalent bond means they are no longer a single molecule, but rather two separate atoms … well, except that they’re not even atoms any more …

The atoms no longer just have just a little bit (δ) of charge. The one on the left has lost an entire electron’s worth of charge. Losing negative charge means that overall it is now (properly, not just a little bit) positively charged.

The one on the right has a whole electron’s worth of negative charge more than it needs to cancel out its positive nuclues. It is now (properly) negatively charged.

Because they are (properly!) charged, we no longer call them atoms. Instead they are ions.

Water experiences this sort of electron-theft.

Sometimes it exists as the polar H20 molecule, but sometimes its oxygen gets even more greedy and the molecule dissociates into H+ (a hydrogen ion, aka proton), and OH- (a hydroxyl ion).

This dissociation, and the reforming of H20, is happening all the time in normal liquid water.

Note that the ions each have an overall charge, unlike the polar water molecule where the small charges cancel out.

Bigger Molecules

Atoms that are negatively charged due to having extra electrons, or that are positively charged because they lack electrons, often occur in large molecules too.

Where positive charges are found, it helps to think about this as a positively-charged H+ having been added to the molcule.

Here’s an amine group. It’s just part of a larger molecule, which goes off the edge of the image.

It can exist either as —NH2, or it can add on a proton (H+) to become —NH3+.

In living organisms, there are plenty of available protons (remember how water dissociates?). So amine groups like this usually exist as the charged version.

This is not a polar group, it is charged. (Ignore the shape of the electron cloud for this one, the important thing is that there is an overall charge of +1 because of that extra proton).

Electrostatic Interactions

So. Polar molecules are uncharged overall but have just a little bit (δ) of charge in various places. While charged molecules have a big whack of charge due to having lost an electron or having gained a proton. Why is this difference so important?

It’s to do with how polar and charged molecules interact with their environments. It’s not the same.

Hydrogen bonds

Some polar molecules, like DNA, proteins and water, can form hydrogen bonds between the atoms that have the unevenly distributed charges. These are a special type of weak bond.

Water LOVES making hydrogen bonds - this is why it can hold itself together into a droplet.

Notice in the picture that the water molecules remain separate and can still move around. It doesn’t take much to pull a single hydrogen bond apart. Which is why water can still be poured and stirred around with no trouble.

Water is a polar, hydrogen-bonding molecule, and this explains its properties as a solvent. Molecules like glucose can dissolve in water because they are similarly polar and able to make hydrogen bonds.

Hydrogen bonds are also really important in understanding DNA and protein structures.

These molecules hydrogen-bond to themselves. Each individual bond is weak, but multiple repeating bonds work together to hold the structure into shape.

Protein secondary structures are held together by hydrogen bonds.

The image here shows hydrogen bonds between Guanine (G) and Cytosine (C) in DNA. The hydrogen bonds are shown as dotted lines.

To get a feeling for the strength of hydrogen bonds, think about what happens if you spill water on a book, close it, and let it dry. You know how the pages stick together? This is because hydrogen bonds have formed between the pressed-together pages. When you peel them apart, you are pulling these hydrogen bonds apart.

Dissolving ions

Charged ions like Cl-, Na+ and K+ can’t form hydrogen bonds, but they can still dissolve in water because they can form favourable electrostatic interactions with the water molecules.

This diagram shows salt (NaCl) dissolved in water.

Hydrogen bonds are in yellow. And electrostatic interactions between the charged ions and the polar water molecules are shown in green.

See how the water molecules organise around the ions to provide the opposite charge to that presented by the ion.

Non-polar molecules like lipids cannot form electrostatic interactions with water molecules. And so for this reason, non-polar molecules do not dissolve in water. If you could somehow spread a bunch of non-polar molecule through a glass of water, this would cause all sorts of problems because the water molecules next to the non-polar molecules would be unable to satisfy their charges. Water prefers to hydrogen bond to itself, and it would do so, squeezing the the non-polar molecules out to cluster together in undissolved lumps.

Whisk up a teaspoon of oil in a glass of water and watch - you can see this happening. The oil ends up as a separate layer on the surface. Or get a small glass of oil and carefully put a drop of water on top; the water will ball itself up, hydrogen-bonding to itself and minimising the amount of contact it needs to make with the oil.

This is why membranes don’t dissolve in the cytoplasm. The water molecules would much rather hang out with other water molecules where they can make all those lovely hydrogen bonds. Non-polar molecules are called hydrophobic, or “water-hating”, but to be honest that’s a bit unfair because really it’s the water is excluding them, rather than the other way around.

This also means that non-polar molecules can’t act as solvents for polar molecules or charged ions. The reason being the same: they can’t offer any way to satisfy the polar/charged molecules’ hankering for favourable electrostatic interactions. This is why ions (Na+, K+, H+ etc) cannot dissolve into, and move through, membranes. Which is absolutely vital to understand if you want to make sense of how neurons, mitochondria, and chloroplasts function (and many other things in biology besides).

Ionic bonds

Charged molecules have ‘proper’ charges. They interact more strongly through electrostatic interactions to form ionic bonds.

Here is a positively charged amine group (NH3+) forming an ionic bond with a negatively charged hydroxyl group (OH-).

They are not sharing an electron cloud, so this is not a covalent bond.

Maybe these charged groups are both parts of the same protein (ie from different R groups). If so, this interaction may be important in defining the protein’s tertiary structure.

Or maybe it’s an interaction between an enzyme and its substrate?

Ionic bonds are really important for controlling what binds with what - and what doesn’t. Negatively charged groups will repel other negative charges. And positive will repel positive. This prevents incorrect structures forming.

In summary:

Polar molecules are charge-balanced overall but have unevenly distributed electrons. This gives them a little bit ( δ ) of a negative charge on one atom, and a little bit ( δ ) of positive charge on another. In biology, these weak charges often form hydrogen bonds, or favourable electrostatic interactions with ions.

Charged molecules have an overall charge. They have at leat one full unit of charge on at least one atom. (A unit of charge being equal to the magnitude of one electron). These stronger charges can form ionic bonds with each other.

This article was written by Dr Jenny Shipway

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