6th Grade Mean, Median, Spread and Box Plots Test Solutions and Scoring (PDF)

6th Grade math test solutions: Mean, Median, Spread and Box Plots – Maths PDF

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This center spread test answers for 6th Grade covers mean, median, spread and box plots (Common Core 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d), with a free PDF to print.

Use this key to score the test out of 20 points. Each solution is fully worked, and the scoring line explains how to award each point and partial credit.

Grade 6 · Common Core State Standards: 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d

Center spread test answers: worked solutions

Question 1 – Mean and median [2 pts]

Mean: \(35 \div 5 = 7\). Ordered 5, 6, 7, 8, 9: median 7.

Scoring: 1 point for the mean; 1 point for the median.

Question 2 – Even-sized set [2 pts]

Ordered: 3, 4, 6, 6, 7, 10; median \(\frac{6 + 6}{2} = 6\). Mode 6.

Scoring: 1 point for each.

Question 3 – MAD [2 pts]

Mean 7. Distances 3, 1, 1, 3. MAD \(\frac{8}{4} = 2\).

Distances from 7: 3, 1, 1, 3.

Scoring: 1 point for the mean; 1 point for the MAD.

Question 4 – Box plot [2 pts]

Min 1, Q1 3.5, median 6.5, Q3 9.5, max 12.

Five-number summary.

Scoring: 1 point for the summary; 1 point for the box plot.

Question 5 – Read a box plot [2 pts]

Median 35; range \(60 – 20 = 40\); IQR \(50 – 30 = 20\).

Scoring: 1 point for the median; 1 point for the range and IQR.

Question 6 – Outlier [2 pts]

Mean \(118 \div 6 \approx 19.7\); median \(\frac{12 + 12}{2} = 12\).

The median is better.

Scoring: 1 point for the values; 1 point for the choice and reason.

Question 7 – Missing score [2 pts]

Total \(6 \cdot 82 = 492\). Five scores total \(78 + 85 + 90 + 76 + 80 = 409\).

\(492 – 409 = 83\).

Scoring: 1 point for the total; 1 point for 83.

Question 8 – Compare [3 pts]

Boys: median 15, IQR \(18 – 12 = 6\). Girls: median 16, IQR \(17 – 13 = 4\).

Girls have the greater median. Boys have the greater IQR.

Scoring: 1 point for the medians and IQRs; 1 point for each conclusion.

Question 9 – Describe the data [3 pts]

Mean: \(118 \div 7 \approx 16.9\). Median: 13.

First six: mean \(77 \div 6 \approx 12.8\).

The outlier 41 pulls the mean up, so report the median 13.

Scoring: 1 point for the mean and median; 1 point for the discussion of the outlier; 1 point for the choice.

Total score

Total

20 points

Key facts behind this center spread test answers

Key facts

Mean = sum divided by the number of values; median = middle value.
Range = greatest minus least; IQR = Q3 minus Q1.
MAD is the average distance of the values from the mean.
A box plot shows the minimum, Q1, median, Q3, and maximum.
Outliers pull the mean but not the median.

How to use this center spread 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 6 chapters: Grade 6 math.

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