S4.2.7 Chapter 7
Variation
Why are no two people exactly alike, even in one family?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
- Sort features into ones caused by genes, surroundings or both
- Collect hand spans from family and friends and plot a histogram
Look at the people in one family. They have things in common, but no two are exactly alike. The differences between living things of the same kind are called variation.
Variation has two causes. Some features come from genes: they are inherited. Some come from the environment, which means the surroundings and everything that happens to a living thing. Many features come from both.
Take height. Your genes set a range for how tall you can grow. Food, health and sleep decide where in that range you end up. Take body mass. Genes affect it, and so do the food you eat and the exercise you take.
Identical twins give us a clue. They start from one fertilised egg, so they have almost exactly the same DNA. When identical twins differ, for example in mass, the cause is mostly the environment.
There are two kinds of variation. Some features fall into separate groups, with nothing in between. Your blood group is A, B, AB or O. This is discontinuous variation. Other features can take any value in a range. Height, mass and hand span are like this. This is continuous variation.
For continuous variation we use a histogram. We split the range into classes of equal width. We count how many values fall in each class. This count is the frequency. The bars touch, because the end of one class is the start of the next.
A value on a boundary goes in the higher class. So 20.0 cm goes in the class from 20 to 22 cm, and not in 18 to 20 cm. Here are the hand spans of 30 people. A span is the distance from the tip of the thumb to the tip of the little finger. The hand is spread wide.
Worked example
The table shows 30 hand spans in cm. How many are in the class from 18 to 20 cm?
- The class 18 to 20 cm includes 18.0 and every value up to, but not including, 20.0.
- They are 18.0, 18.3, 18.6, 18.9, 19.0, 19.2, 19.4, 19.5, 19.7 and 19.9.
- There are 10 values in the class.
Answer: 10 people
Worked example
Use the histogram. How many of the 30 people have a hand span of 20 cm or more?
- Spans of 20 cm or more are in the classes 20 to 22 cm and 22 to 24 cm.
- Read the bars. The class 20 to 22 cm has a bar of height 8.
- The class 22 to 24 cm has a bar of height 5.
- The number of people is 8 + 5 = 13.
Answer: 13 people
A histogram looks like a bar chart, but there are two differences. Its bars touch. Its horizontal axis is a number line, so the classes have no gaps. In this book the classes are of equal width, so the height of each bar is the frequency. A bar chart for separate groups has gaps between its bars.
Try it
Measure hand spans
You need: a ruler, or a strip of paper marked in centimetres, a pencil, an old sheet of paper, family and friends, at least 15 if you can.
Be safe: Measure only people who agree. Do not touch anyone's hand without being asked. Keep the pencil away from faces.
- Ask each person first. Only measure people who agree.
- Ask a person to spread one hand flat on the paper, with the fingers wide. Put a dot at the tip of the thumb and a dot at the tip of the little finger.
- Measure between the dots, to the nearest 0.5 cm. Use the same hand for everyone. Write the numbers in a list.
- Choose classes of equal width, such as 2 cm. Count how many spans fall in each class. Draw the bars so that they touch.
What you will see: Most spans fall near the middle, with fewer at both ends. If your numbers differ, that is variation too. Adults and children have different ranges, so a mixed group gives a wider spread.
A wrong idea many people have
Your genes decide everything about you.
Why it feels right: We say that a feature "runs in the family", so it can seem that nothing else matters.
The test that breaks it: Identical twins have almost the same genes. Yet they can differ in mass, in scars and in the language they speak. Those differences come from the environment.
What is true: Genes decide a great deal. But for many features, genes and the environment work together. Some features, such as a scar, have nothing to do with genes.
Key words
- variation
- the differences between living things of the same kind.
- environment
- the surroundings of a living thing and everything that happens to it.
- continuous variation
- variation in which a feature can take any value in a range, such as height.
- discontinuous variation
- variation in which a feature falls into separate groups, such as blood group.
- histogram
- a chart for continuous data, with bars that touch. With classes of equal width, the height of a bar is its frequency.
- frequency
- the number of values that fall in a class.
Back to your guess
The answer is C: Because of both: their genes and the surroundings in which they live and grow.
Both. Genes give a person their starting point. Food, health, learning and chance then add to it. For many features, the two work together.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
Which feature is caused by the environment and not by genes?
See the answer
A scar on the knee
A scar is caused by an injury, and so by the environment. No gene makes it.
- If you chose A: Blood group is inherited. The environment does not change it.
- If you chose C: The basic shape of a finger is inherited. An injury can change it, but the shape starts with genes.
Which feature is caused by both genes and the environment?
See the answer
Height
Genes set a range for how tall a person can be. Food, health and sleep decide where in the range they end up.
- If you chose B: Blood group depends on genes only. Food and health do not change it.
- If you chose C: A person learns the language they hear. That is the environment, not genes.
Two identical twins are different in body mass. What is the most likely cause?
See the answer
The environment, such as food and exercise
The twins have almost the same genes, so a difference between them is most likely caused by surroundings.
- If you chose A: Identical twins have almost exactly the same DNA, so genes are not the likely cause.
- If you chose B: A Punnett square predicts how genes pass from parents. The twins have the same genes already. Go to S4.2.5.
- If you chose C: A carrier has a recessive allele that is hidden. It does not change body mass. Go to S4.2.6.
Blood group can be A, B, AB or O, and nothing in between. What kind of variation is this?
See the answer
Discontinuous variation
The groups are separate, with nothing in between. This is discontinuous variation.
- If you chose B: Continuous variation means any value in a range, such as height. Blood group falls in separate groups.
- If you chose C: Inherited features can vary between people. People have different blood groups, so there is variation.
Look at the histogram. In which class is the tallest bar?
See the answer
18 to 20 cm
The bar for 18 to 20 cm reaches 10, which is more than any other bar.
- If you chose A: That bar reaches 5. Look for the bar that reaches the highest.
- If you chose B: That bar reaches 8. One bar is higher.
Why do the bars of a histogram of hand spans touch?
See the answer
Hand span can take any value in a range, so one class begins where the last ends.
There is no gap between 19.9 cm and 20.0 cm, so the bars have no gap either.
- If you chose A: Space is not the reason. The reason is about the numbers.
- If you chose C: Every bar is the same feature, hand span. Each bar is a class of values of it.
From an earlier chapter
Two carriers of sickle cell disease have a child. What is the chance that the child is also a carrier?
See the answer
1 in 2
Two of the four boxes read Hh. So the chance is 2 out of 4, which is 1 in 2.
Hand spans from 12 cm to 24 cm are put in 6 classes of equal width. How wide is each class?
See the answer
2 cm
The range is 24 − 12 = 12 cm. Six equal classes share it, so each is 12 ÷ 6 = 2 cm wide.
The classes of a hand span histogram start at 14 cm and are 2 cm wide. In which class is a hand span of 17.3 cm? Write the class as two numbers.
See the answer
16 to 18 cm
17.3 is more than 16 and less than 18, so it is in the class from 16 to 18 cm.
Keep it
Copy this into your exercise book.
Variation comes from genes, the environment, or both. Blood group falls in separate groups. Height can take any value in a range. A histogram has touching bars. With classes of equal width, the height of a bar is its frequency.
Draw: A histogram of hand spans with classes of 2 cm and touching bars, with both axes named.