Chapter 7 of 8

All 8 chapters
  1. 1DNA, genes and chromosomes, readunderstood
  2. 2The structure of DNA, readunderstood
  3. 3Meiosis and sex cells, readunderstood
  4. 4Boy or girl: X and Y, readunderstood
  5. 5Dominant and recessive, readunderstood
  6. 6Family trees and genetic disorders, readunderstood
  7. 7Variation, readunderstood
  8. 8Mutation and genetic engineering, readunderstood

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.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

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.

A table with the columns Feature and Cause. Blood group is genes. Scar is environment. Language is environment. Height is both. Body mass is both.FeatureCauseblood groupgenesscarenvironmentlanguageenvironmentheightbothbody massboth
Environment means the surroundings and what happens to a person. Language here means the language a person speaks. Genes decide your blood group, and a scar comes from an injury.

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.

A bar chart of the blood groups in a class of 40 learners. The axis is labelled number of learners, with a scale from 0 to 20 in steps of 5. The bar for O reaches 17. The bar for A reaches 15. The bar for B reaches 6. The bar for AB reaches 2.05101520OABABnumber of learners
Example numbers for a class of 40. The shares of each group differ from place to place. Separate groups give separate bars with gaps. Each learner is in exactly one group.

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.

A table of 30 hand spans in four columns, each headed cm. Read across the rows, the values are 15.2, 15.8, 16.4, 16.9, 17.1, 17.5, 17.8, 18.0, 18.3, 18.6, 18.9, 19.0, 19.2, 19.4, 19.5, 19.7, 19.9, 20.0, 20.2, 20.4, 20.6, 20.9, 21.1, 21.3, 21.8, 22.0, 22.4, 22.7, 23.1, 23.6.cmcmcmcm15.215.816.416.917.117.517.818.018.318.618.919.019.219.419.519.719.920.020.220.420.620.921.121.321.822.022.422.723.123.6
The hand spans of 30 people, in cm. Read across each row.

Worked example

The table shows 30 hand spans in cm. How many are in the class from 18 to 20 cm?

  1. The class 18 to 20 cm includes 18.0 and every value up to, but not including, 20.0.
  2. They are 18.0, 18.3, 18.6, 18.9, 19.0, 19.2, 19.4, 19.5, 19.7 and 19.9.
  3. There are 10 values in the class.

Answer: 10 people

A table with the columns Class (cm) and People. 14 to 16 has 2. 16 to 18 has 5. 18 to 20 has 10. 20 to 22 has 8. 22 to 24 has 5.Class (cm)People14 to 16216 to 18518 to 201020 to 22822 to 245
The frequency of each class. All five classes are 2 cm wide.
A histogram of hand spans. The axis along the bottom is labelled hand span (cm) with the classes 14 to 24 in steps of 2. The axis up the side is labelled number of people, with a scale from 0 to 12 in steps of 2. The bars touch. They reach 2, 5, 10, 8 and 5.024681012141618202224number of peoplehand span (cm)
Most hand spans are near the middle. Fewer are very small or very large. This is a common shape for continuous variation.

Worked example

Use the histogram. How many of the 30 people have a hand span of 20 cm or more?

  1. Spans of 20 cm or more are in the classes 20 to 22 cm and 22 to 24 cm.
  2. Read the bars. The class 20 to 22 cm has a bar of height 8.
  3. The class 22 to 24 cm has a bar of height 5.
  4. 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.

  1. Ask each person first. Only measure people who agree.
  2. 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.
  3. Measure between the dots, to the nearest 0.5 cm. Use the same hand for everyone. Write the numbers in a list.
  4. 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.

If you cannot try it, this is what happens.
Empty axes for a histogram. The axis along the bottom is labelled hand span (cm) with the classes 14 to 24 in steps of 2. The axis up the side is labelled number of people, with a scale from 0 to 12 in steps of 2. There are no bars yet.024681012141618202224number of peoplehand span (cm)

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.

  1. Which feature is caused by the environment and not by genes?

    Tap your answer.

    1. Not this one. Blood group is inherited. The environment does not change it. Try another.

    2. Yes, that is right. A scar is caused by an injury, and so by the environment. No gene makes it.

    3. Not this one. The basic shape of a finger is inherited. An injury can change it, but the shape starts with genes. Try another.

    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.

  2. Which feature is caused by both genes and the environment?

    Tap your answer.

    1. Yes, that is right. Genes set a range for how tall a person can be. Food, health and sleep decide where in the range they end up.

    2. Not this one. Blood group depends on genes only. Food and health do not change it. Try another.

    3. Not this one. A person learns the language they hear. That is the environment, not genes. Try another.

    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.

  3. Two identical twins are different in body mass. What is the most likely cause?

    Tap your answer.

    1. Not this one. Identical twins have almost exactly the same DNA, so genes are not the likely cause. Try another.

    2. Not this one. A Punnett square predicts how genes pass from parents. The twins have the same genes already. Go to S4.2.5. Try another.

    3. Not this one. A carrier has a recessive allele that is hidden. It does not change body mass. Go to S4.2.6. Try another.

    4. Yes, that is right. The twins have almost the same genes, so a difference between them is most likely caused by surroundings.

    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.

  4. Blood group can be A, B, AB or O, and nothing in between. What kind of variation is this?

    Tap your answer.

    1. Yes, that is right. The groups are separate, with nothing in between. This is discontinuous variation.

    2. Not this one. Continuous variation means any value in a range, such as height. Blood group falls in separate groups. Try another.

    3. Not this one. Inherited features can vary between people. People have different blood groups, so there is variation. Try another.

    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.

  5. Look at the histogram. In which class is the tallest bar?

    A histogram of hand spans. The axis along the bottom is labelled hand span (cm) with the classes 14 to 24 in steps of 2. The axis up the side is labelled number of people, with a scale from 0 to 12 in steps of 2. The bars touch. They reach 2, 5, 10, 8 and 5.024681012141618202224number of peoplehand span (cm)
    Tap your answer.

    1. Not this one. That bar reaches 5. Look for the bar that reaches the highest. Try another.

    2. Not this one. That bar reaches 8. One bar is higher. Try another.

    3. Yes, that is right. The bar for 18 to 20 cm reaches 10, which is more than any other 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.

  6. Why do the bars of a histogram of hand spans touch?

    Tap your answer.

    1. Not this one. Space is not the reason. The reason is about the numbers. Try another.

    2. Yes, that is right. There is no gap between 19.9 cm and 20.0 cm, so the bars have no gap either.

    3. Not this one. Every bar is the same feature, hand span. Each bar is a class of values of it. Try another.

    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.

  7. From an earlier chapter

    Two carriers of sickle cell disease have a child. What is the chance that the child is also a carrier?

    Tap your answer.

    1. Not this one. That is the chance of the disease. Two boxes of four read Hh, the carrier. Go to S4.2.6. Try another.

    2. Not this one. Both parents can pass on h. A child who gets one H and one h is a carrier. Go to S4.2.6. Try another.

    3. Yes, that is right. Two of the four boxes read Hh. So the chance is 2 out of 4, which is 1 in 2.

    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.

    • If you chose A: That is the chance of the disease. Two boxes of four read Hh, the carrier. Go to S4.2.6.
    • If you chose B: Both parents can pass on h. A child who gets one H and one h is a carrier. Go to S4.2.6.

  8. 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.

  9. 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.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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