Scatter Graphs & Correlation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Scatter Graphs and Correlation

Mathematics · Data & Statistics · ages 13-14
Name ______________________   Date ____________

  1. Four scatter graphs were drawn. Which one shows a negative correlation?

    • The points fall from the upper left down to the lower right
    • The points climb from the lower left up to the upper right
    • The points are spread randomly with no clear direction
    • All the points sit exactly on a horizontal line

  2. Maya plotted the number of hours of TV watched and the test score for each of her 10 classmates. The correlation number r came out as -0.85. What kind of correlation is this?

    • Positive correlation
    • Negative correlation
    • No correlation
    • It cannot be determined

  3. A scatter graph shows points that generally rise from left to right. What is this called?

    • Positive correlation
    • Negative correlation
    • No correlation

  4. On a scatter graph, each point shows two measurements together, not just one.

    Circle one:   True   False

  5. Why do we draw a line of best fit instead of joining the points dot to dot?

    • It shows the general trend without matching every small bump in the data
    • It always passes through every single point exactly
    • It changes what type of correlation the graph shows

  6. A correlation coefficient, r, is calculated from a scatter plot. What does it measure?

    • The direction and strength of the straight-line relationship between the two variables
    • The exact y value you get for any chosen x value
    • The average of all the x and y values added together
    • The total number of points plotted on the graph

  7. If the correlation between two variables is 0, the two variables are not related at all.

    Circle one:   True   False

  8. A student plots pages read each night against time spent on the phone, and the points scatter with no clear trend. What does this show?

    • Positive correlation
    • Negative correlation
    • No correlation

  9. Ravi's data on revision hours only ranges from 0 to 10 hours, but he uses his line of best fit to predict a score for 40 hours of revision. What is the problem?

    • A line of best fit can only be used to predict scores, never hours
    • The prediction goes far beyond the data he measured, so it may not be reliable
    • There is no problem; lines of best fit work for any value

  10. Ice-cream sales and shark attacks both rise in summer, showing positive correlation. Does eating ice cream cause shark attacks?

    • The correlation is actually negative, not positive
    • Yes, since the two are positively correlated, one must cause the other
    • No, a third factor, warmer weather, brings more swimmers and more ice-cream buyers
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Answer key

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Scatter Graphs and Correlation W1-mt_8atyuvPUZc-s1

  1. The points fall from the upper left down to the lower right · Negative correlation means as one variable increases the other decreases, so the points trend downward from left to right.
  2. Negative correlation · A negative r means that as one variable goes up, the other tends to go down, so this is negative correlation.
  3. Positive correlation · When one value goes up and the other tends to go up too, that's positive correlation.
  4. True · Every point is plotted using an x-value and a y-value, one for each variable being compared.
  5. It shows the general trend without matching every small bump in the data · The line follows the overall trend. It doesn't need to hit every point, and usually won't.
  6. The direction and strength of the straight-line relationship between the two variables · r describes how strongly and in which direction two variables follow a linear pattern. It does not give exact values, averages, or counts.
  7. False · False. Correlation only measures straight-line relationships. Two variables can have r = 0 and still follow a strong curved pattern.
  8. No correlation · With no clear upward or downward trend, the two variables show no correlation.
  9. The prediction goes far beyond the data he measured, so it may not be reliable · Predicting so far outside the measured range is risky. The pattern might not hold that far beyond the actual data.
  10. No, a third factor, warmer weather, brings more swimmers and more ice-cream buyers · Correlation shows two things change together. It doesn't prove one causes the other. Here, hot weather affects both.
Worksheet · LightMySky