8th Grade Two-Way Tables and Relative Frequency Test Solutions and Scoring (PDF)

8th Grade math test solutions: Two-Way Tables and Relative Frequency – Maths PDF

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This two way tables test answers for 8th Grade covers two-way tables and relative frequency (Common Core 8.SP.A.4), with a free PDF to print.

Use this answer key to score the two-way tables test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.SP.A.4

Two way tables test answers: worked solutions

Question 1 – Read the table [3 pts]

Totals.

\(24 + 6 = 30\)
\(6 + 40 = 46\)
24

Scoring: 1 point each.

Question 2 – Complete a table [3 pts]

Grade 7: \(28 + 12 = 40\). Soccer: \(28 + 32 = 60\). Total: \(40 + 50 = 90\).

Scoring: 1 point for each total.

Question 3 – Relative frequencies [3 pts]

Chess: \(\frac{24}{30} = 80\%\). No chess: \(\frac{30}{70} \approx 42.9\%\).

Scoring: 1 point for the setup, 1 point for each percent.

Question 4 – Association [2 pts]

Yes. 80% versus 42.9% is a large difference, so chess players are much more likely to like math in this sample.

Scoring: 1 point for yes. 1 point for citing the percents.

Question 5 – Segmented bars [3 pts]

The chess group (80%). The bars are very different, which shows an association.

Scoring: 1 point for the group, 2 points for the explanation.

Question 6 – Build a table [2 pts]

Band and sport.

Scoring: 1 point for the four cells. 1 point for the totals.

Question 7 – Explain [1 pt]

Counts depend on the group size, but percents show the rate for each group.

Scoring: 1 point for a correct explanation.

Question 8 – Cause [3 pts]

Not necessarily. The table shows an association. Other factors, such as distance or schedule, might explain it.

Scoring: 1 point for a clear explanation.

Total score

Total

20 points

Key facts behind this two way tables test answers

Key facts

Joint frequencies are the counts inside the table; marginal frequencies are the totals.
Relative frequency = count ÷ total, usually as a percent.
Row percents compare groups defined by the rows.
If row percents differ a lot, the variables are associated.
Association does not prove that one variable causes the other.

How to use this two way tables test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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