7th Grade Comparing Two Populations Test Solutions and Scoring (PDF)

7th Grade math test solutions: Comparing Two Populations – Maths PDF

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This comparing populations test answers for 7th Grade covers comparing two populations (Common Core 7.SP.B.3, 7.SP.B.4), with a free PDF to print.

Use this answer key and scoring guide to grade the comparing populations test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

Grade 7 · Common Core State Standards: 7.SP.B.3, 7.SP.B.4

Comparing populations test answers: worked solutions

Question 1 – Mean and median [2 pts]

Mean: \(54\div 6=9\).

Median: \((9+9)\div 2=9\).

mean 9; median 9

Scoring: 1 point for each.

Question 2 – MAD [2 pts]

Mean: 6. Distances: 4, 2, 0, 2, 4; sum 12.

\(12\div 5=2.4\)

2.4

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

Question 3 – Compare dot plots [2 pts]

Team B is more spread out.

Range A: \(9-5=4\). Range B: \(13-3=10\).

Team B; ranges 4 and 10

Scoring: 1 point for the team with an explanation; 1 point for both ranges.

Question 4 – Quartiles [2 pts]

Lower half: 20, 22, 25, 28; Q1 = \((22+25)\div 2=23.5\).

Upper half: 30, 31, 35, 40; Q3 = \((31+35)\div 2=33\).

IQR = \(33-23.5=9.5\)

Q1 = 23.5; Q3 = 33; IQR = 9.5

Scoring: 1 point for Q1 and Q3; 1 point for the IQR.

Question 5 – Compare box plots [2 pts]

Medians: 15 and 20; Plant B is 5 cm higher.

IQRs: \(18-12=6\) and \(23-17=6\), the same.

Plant B; equal IQRs

Summary.

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

Question 6 – Difference in MADs [2 pts]

\(85-70=15\), and \(15\div 5=3\) MADs.

The groups are clearly different because the gap is large compared with the spread.

3 MADs

Scoring: 1 point for the multiple; 1 point for the meaning.

Question 7 – Informal inference [2 pts]

The medians differ by 6 minutes, about 1 IQR, so School A students probably travel longer.

Taking larger or repeated random samples would strengthen the conclusion.

School A students probably travel longer

Scoring: 1 point for the conclusion; 1 point for the strengthening step.

Question 8 – Two classes [3 pts]

Class A: 84. Class B: 84.
Class A: Q1 80, Q3 88, IQR 8. Class B: Q1 70, Q3 98, IQR 28.
Class A, because its IQR is much smaller.

Five-number summary details.

Scoring: 1 point for each part.

Question 9 – Two runners [3 pts]

\(200\div 5=40\) minutes for each.
Runner 1: distances 5, 2, 0, 2, 5, sum 14, MAD \(14\div 5=2.8\). Runner 2: distances 12, 6, 0, 7, 11, sum 36, MAD \(36\div 5=7.2\).
Runner 1 is more consistent because the MAD is smaller.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this comparing populations test answers

Key facts

Center: mean or median. Spread: MAD, range, or IQR.
MAD is the mean of the distances from the mean.
A box plot shows the minimum, Q1, median, Q3, and maximum; IQR = Q3 – Q1.
Express the difference in centers as a multiple of the variability.
Random samples support informal inferences about populations.

How to use this comparing populations 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 7 chapters: Grade 7 math.

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