Victorian Curriculum Year 10A - 2020 Edition
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11.07 Investigating data with scatter plots
Lesson

Interpreting bivariate data

When we have bivariate data, we want to determine what sort of relationship the two variables have. As the independent variable ($x$x-axis) changes notice how the dependent variable ($y$y-axis) tends to change. Just by observation, we may notice the following:

  • A simple relationship: if the distribution of points appears to follow a trend either linear or non-linear depending on if the points appear to follow the shape of a line or not.

    Consider being given an $x$x-value that doesn't correspond to any data point we have. Does the data set give us an idea of what $y$y-value that point should have to fit in with the rest of the data? If yes there might be a relationship. If not, there might be no relationship between the variables.
     
  • Outliers: in a scatterplot, any data points that are very different from the other data points will be quite obvious especially if the rest of the points appear to have a relationship.
Causal relationships

Even when two variables have a relationship, it may not be a causal relationship. We cannot say for sure that a change in the value of $x$x causes $y$y to change or that the value of $y$y causes a corresponding value of $x$x even when a relationship is apparent. It may be that both $x$x and $y$y have a relationship with some other hidden variable, which creates an indirect relationship between $x$x and $y$y.

Practice questions

question 1

The scatter plot shows the relationship between sea temperature and the amount of healthy coral.

  1. Which variable is the dependent variable?

    Sea temperature

    A

    Level of healthy coral

    B

    Sea temperature

    A

    Level of healthy coral

    B
  2. Which variable is the independent variable?

    Sea temperature

    A

    Level of healthy coral

    B

    Sea temperature

    A

    Level of healthy coral

    B

question 2

The scatterplot shows the height and weight of six students. Use the plot to answer the questions.

Loading Graph...

  1. How tall is the student who weighs $45$45kg?

  2. How tall is the tallest student?

question 3

The price of ten houses is graphed against the house's land area below.

Describe the relationship between land area and house price in the data.

Loading Graph...

  1. As land area increases, house price decreases.

    A

    As land area increases, house price increases.

    B

    Land area has no effect on house price.

    C

    As land area increases, house price decreases.

    A

    As land area increases, house price increases.

    B

    Land area has no effect on house price.

    C

Outcomes

VCMSP352

Use scatter plots to investigate and comment on relationships between two numerical variables

VCMSP353

Investigate and describe bivariate numerical data where the independent variable is time.

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