Grade 8 · Math

Describe association in paired data

Describe an upward, downward or unclear overall trend in paired measurements without treating association as proof of cause.

6 authored questions + worked example

Worked example

Paired measurements: (1, 2), (2, 3), (3, 5), (4, 7), (5, 8).

Which description best matches the overall direction of these paired data?

Answer & why

Answer: an upward trend

The second values generally increase as the first values increase. Association in a data set does not by itself establish cause.

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All questions

All 6 authored questions for this skill.

Question 1

Paired measurements: (1, 2), (2, 5), (3, 2), (4, 5), (5, 2).

Which description best matches the overall direction of these paired data?

  1. an upward trend
  2. a downward trend
  3. no clear upward or downward trend
  4. proof that the first variable causes the second
A hint

Read the pairs from smaller to larger first coordinates and look for an overall direction.

Answer & why

Answer: no clear upward or downward trend

The second values alternate rather than generally moving upward or downward. Association in a data set does not by itself establish cause.

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Question 2

Paired measurements: (1, 1), (2, 3), (3, 4), (4, 6), (5, 9).

Which description best matches the overall direction of these paired data?

  1. proof that the first variable causes the second
  2. an upward trend
  3. no clear upward or downward trend
  4. a downward trend
A hint

Read the pairs from smaller to larger first coordinates and look for an overall direction.

Answer & why

Answer: an upward trend

Higher first values are paired with higher second values in these data. Association in a data set does not by itself establish cause.

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Question 3

Paired measurements: (1, 10), (2, 8), (3, 6), (4, 5), (5, 1).

Which description best matches the overall direction of these paired data?

  1. an upward trend
  2. a downward trend
  3. no clear upward or downward trend
  4. proof that the first variable causes the second
A hint

Read the pairs from smaller to larger first coordinates and look for an overall direction.

Answer & why

Answer: a downward trend

Higher first values are paired with lower second values in these data. Association in a data set does not by itself establish cause.

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Question 4

Paired measurements: (1, 5), (2, 2), (3, 7), (4, 2), (5, 5).

Which description best matches the overall direction of these paired data?

  1. proof that the first variable causes the second
  2. an upward trend
  3. no clear upward or downward trend
  4. a downward trend
A hint

Read the pairs from smaller to larger first coordinates and look for an overall direction.

Answer & why

Answer: no clear upward or downward trend

The values fluctuate with no overall upward or downward direction. Association in a data set does not by itself establish cause.

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Question 5

Paired measurements: (1, 2), (2, 3), (3, 5), (4, 7), (5, 8).

Which description best matches the overall direction of these paired data?

  1. an upward trend
  2. a downward trend
  3. proof that the first variable causes the second
  4. no clear upward or downward trend
A hint

Read the pairs from smaller to larger first coordinates and look for an overall direction.

Answer & why

Answer: an upward trend

The second values generally increase as the first values increase. Association in a data set does not by itself establish cause.

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Question 6

Paired measurements: (1, 9), (2, 7), (3, 6), (4, 4), (5, 2).

Which description best matches the overall direction of these paired data?

  1. a downward trend
  2. proof that the first variable causes the second
  3. an upward trend
  4. no clear upward or downward trend
A hint

Read the pairs from smaller to larger first coordinates and look for an overall direction.

Answer & why

Answer: a downward trend

The second values generally decrease as the first values increase. Association in a data set does not by itself establish cause.

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