Geometry and Statistics Assessments

b) Area of playground. (1 pt)

Length = \(x + 5\)
Length = \(10 + 5 = 15\) m
Width = 8 m
Area = \(15 \times 8 = 120 \text{ m}^2\)
[1 pt area with units]

c) Sodding cost. (2 pts)

Cost = Area \(\times\) $4
Area = 120 \(\text{m}^2\)
Cost = \(120 \times \$4 = \$480\)

[1 pt setup, 1 pt answer]

Geometry Quarter 1 Assessment Suite • Quiz 1 Answer Key Page 2 of 2

D \(\overline{EM} \cong \overline{EF}\)

Geometry Quarter 1 Assessment Suite Page 2 of 5

Quiz 2 • Multiple Choice Continued

8. Point N is the midpoint of segment GH. If \(GN = 2x\) and \(NH = x + 9\), what is the length of segment \(GH\)?

G N H 2x x + 9

A 9

B 18

C 36

D 45

9. What is the midpoint of the segment with endpoints A(2, 4) and B(8, 10)?

A (10, 14)

B (5, 7)

C (3, 3)

D (6, 7)

10. What is the midpoint of the segment with endpoints C(−6, 3) and D(4, 7)?

A (−1, 5)

B (−5, 2)

C (−1, 2)

D (5, −1)

11. Segment GH is graphed below with endpoints G(2, 5) and H(−4, −1). What is the midpoint of segment GH?

G(2,5) H(-4,-1)

A (−2, 4)

B (3, 2)

C (−1, 3)

D (−1, 2)

Geometry Quarter 1 Assessment Suite Page 3 of 5

Quiz 2 • Multiple Choice Continued

12. Which of the following correctly names the angle below?

B A C

A \(\angle BAC\)

B \(\angle ABC\)

C \(\angle ACB\)

D \(\angle CAB\)

13. In angle \(\angle XYZ\), which point is the vertex of the angle?

A Point X

B Point Z

C Point Y

D No vertex

14. In the figure below, three rays share vertex Q. Which name clearly identifies the marked angle (the angle between ray QP and ray QS)?

Q P S R ?

A \(\angle PQS\)

B \(\angle Q\)

C \(\angle S\)

D \(\angle PSQ\)

15. An angle is formed by ray BA and ray BC. What is another name for this angle?

A \(\angle ABC\)

B \(\angle ACB\)

C \(\angle BAC\)

D \(\angle CAB\)

Geometry Quarter 1 Assessment Suite Page 4 of 5

Section 2: Open-Ended Responses (2 Questions • 5 Points Each)

16. In the figure below, points G, H, J, and K are on the same line. If \(GH = x + 4\), \(HJ = 2x\), \(JK = x + 9\), and \(GK = 45\):

G H J K x + 4 2x x + 9 GK = 45

a) Write an equation for segment addition and solve for \(x\). (3 pts)

b) Find the length of segment \(HJ\). (2 pts)

17. Segment AB has endpoints A(−2, 6) and B(4, −2). Point M is the midpoint of segment AB.

A(-2,6) B(4,-2)

a) Use the midpoint formula to find the coordinates of point M. Show your work. (3 pts)

b) In one sentence, explain what it means for M to be the midpoint of segment AB. (2 pts)

Geometry Quarter 1 Assessment Suite Page 5 of 5

a) Use midpoint formula to findcoordinates of point M. (3 pts)

Endpoints: \(A(-2, 6)\) and \(B(4, -2)\)
Formula: \(M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\)
Substitute: \(M = \left( \frac{-2 + 4}{2}, \frac{6 + (-2)}{2} \right)\)
Simplify: \(M = \left( \frac{2}{2}, \frac{4}{2} \right) = (1, 2)\)
[1 pt correct formula/substitution, 1 pt arithmetic steps, 1 pt correct coordinates M(1, 2)]

b) Explain what it means for M to be the midpoint of segment AB. (2 pts)

Accept any reasonable conceptual statement, such as:
• Point M is exactly halfway between endpoint A and endpoint B.
• Point M splits segment AB into two equal/congruent pieces (\(AM = MB\)).

[2 pts clear explanation of equal parts or halfway property, 1 pt if partially explained]

Geometry Quarter 1 Assessment Suite • Quiz 2 Answer Key Page 2 of 2

A \(\overrightarrow{XY}\) and \(\overrightarrow{XZ}\)

B \(\overrightarrow{YX}\) and \(\overrightarrow{ZX}\)

C \(\overline{XY}\) and \(\overline{XZ}\)

D \(\overleftrightarrow{YX}\) and \(\overleftrightarrow{XZ}\)

9. The rectangle below has a length of 12 inches and a width of \((x + 3)\) inches. The perimeter is 40 inches. What is the value of \(x\)?

12 in \((x + 3)\) in

A 3

B 5

C 8

D 10

10. The sides of the triangle below measure \(x\), \((x + 4)\), and \((2x - 1)\). The perimeter of the triangle is 35 units. What is the value of \(x\)?

\(x\) \(x + 4\) \(2x - 1\)

A 7

B 9

C 8

D 15

Geometry Quarter 1 Assessment Suite • Test 1 Page 2 of 7

Test 1 • Multiple Choice Continued

11. A square park has a perimeter of 64 feet. What is the length of one side of the park?

A 8 feet

B 16 feet

C 32 feet

D 256 feet

12. A rectangle has a perimeter of 48 cm. Its length is \(2x\) cm and its width is 8 cm. What is the value of \(x\)?

A 4

B 8

C 12

D 16

13. The perimeter of an equilateral triangle is 27 cm. If one side measures \((2x - 3)\) cm, what is the value of \(x\)?

A 3

B 6

C 5

D 9

14. A rectangular frame has length \((2x + 5)\) cm and width \((x + 2)\) cm. If its perimeter is 44 cm, find \(x\).

A 5

B 4

C 6

D 12

15. A square courtyard has side lengths of \((3x - 2)\) meters. If the perimeter is 40 meters, find the value of \(x\).

A 4

B 10

C 3

D 2

16. A regular pentagon has five equal sides, each measuring \((x + 2)\) cm. If the perimeter of the pentagon is 35 cm, what is the value of \(x\)?

A 7

B 5

C 6

D 9

17. The rectangle below has a length of \((x + 2)\) cm and a width of 6 cm. The area is 54 \(\text{cm}^2\). What is the value of \(x\)?

A 6

B 8

C 9

D 7

Geometry Quarter 1 Assessment Suite • Test 1 Page 3 of 7

Test 1 • Multiple Choice Continued

18. The triangle below has a base of 10 meters and an area of 45 \(\text{m}^2\). What is the height, \(h\), of the triangle?

A 4.5 m

B 9 m

C 18 m

D 35 m

19. The parallelogram below has a base of 8 inches and a height of \(x\) inches. The area is 56 \(\text{in}^2\). What is the value of \(x\)?

A 7

B 8

C 48

D 64

20. A rectangle has an area of 120 square meters. Its length is 15 meters and its width is \((2x - 4)\) meters. What is the value of \(x\)?

A 6

B 8

C 12

D 10

21. The area of a triangle is 24 square inches. If the height is 6 inches, what is the length of its base?

A 8 inches

B 4 inches

C 12 inches

D 16 inches

22. A parallelogram has a base of \(2x\) cm and a height of 5 cm. If its area is 80 \(\text{cm}^2\box\), what is the value of \(x\)?

A 8

B 16

C 4

D 10

23. A rectangular rug has a width of 4 feet and a length of \((x + 3)\) feet. If its area is 32 square feet, what is the value of \(x\)?

A 5

B 8

C 4

D 12

24. What is the distance between point A(1, 2) and point B(4, 6)?

A 25

B 7

C 5

D \(\sqrt{5}\)

Geometry Quarter 1 Assessment Suite • Test 1 Page 4 of 7

Test 1 • Multiple Choice Continued

25. What is the length of the segment with endpoints C(−3, 2) and D(3, −6)?

A 10

B 100

C 14

D 2

26. What is the distance between point G(2, 5) and point H(2, −3)?

A 2

B 4

C 6

D 8

27. Segment JK has endpoints J(1, 1) and K(7, 9). The segment is cut into two equal pieces. What is the length of one of the pieces?

A 10

B 5

C 20

D 2.5

28. What is the length of the segment with endpoints X(−1, 3) and Y(5, 3)?

A 6

B 5

C 4

D 8

29. What is the distance between the origin (0,0) and the point Q(6, 8)?

A 14

B 10

C 48

D \(\sqrt{14}\)

30. What is the length of the segment with endpoints S(2, −2) and T(6, 1)?

A 25

B 5

C 7

D \(\sqrt{7}\)

Geometry Quarter 1 Assessment Suite • Test 1 Page 5 of 7

Section 2: Open-Ended Responses (4 Questions • 5 Points Each)

31. Jerome is building a rectangular garden. The length of the garden is \((x + 4)\) feet and the width is 6 feet. The perimeter of the garden is 44 feet.

\((x + 4)\) ft 6 ft Perimeter = 44 ft

a) Write an equation for the perimeter and solve for \(x\). (2 pts)

b) Find the area of the garden in square feet. (1 pt)

c) Fencing costs $3 per foot. How much will it cost to fence the garden? (2 pts)

32. A park is located at the point (2, 1) on a coordinate map. Jordan’s house is located at (8, 9). Alex’s house is located at (−1, 5). Who lives closer to the park — Jordan or Alex?

Use the distance formula and show your work for BOTH distances to justify your answer. (5 pts total)

Jordan's House to Park distance work: (2 pts)

Alex's House to Park distance work: (2 pts)

Final statement of comparison: (1 pt)

Geometry Quarter 1 Assessment Suite • Test 1 Page 6 of 7

Test 1 • Open-Ended Continued

33. A rectangular dog park has a length of \((x + 6)\) meters and a width of 8 meters. The perimeter of the dog park is 52 meters.

\((x + 6)\) m 8 m Perimeter = 52 m

a) Write an equation for the perimeter and solve for \(x\). (2 pts)

b) Find the area of the dog park in square meters. (1 pt)

c) Landscaping turf costs $5 per square meter. How much will it cost to turf the park? (2 pts)

34. Two delivery trucks start at the central warehouse located at W(1, 2) on a coordinate grid. Truck A delivers to Customer A located at A(4, 10). Truck B delivers to Customer B located at B(9, −4). Which customer is located further from the warehouse?

Use the distance formula and show your work for BOTH distances to justify your answer. (5 pts total)

Warehouse W to Customer A distance work: (2 pts)

Warehouse W to Customer B distance work: (2 pts)

Final statement of comparison: (1 pt)

Geometry Quarter 1 Assessment Suite • Test 1 Page 7 of 7

b) Find Area: (1 pt)

Length = \(x + 4 = 12 + 4 = 16\) ft
Area = \(16 \times 6 = 96 \text{ ft}^2\)
[1 pt correct area]

c) Fencing Cost: (2 pts)

Cost = \(44 \text{ ft} \times \$3/\text{ft} = \$132\)
[1 pt correct multiplication, 1 pt final cost]

Q32 — Distance Formula: Park to Houses Key (5 pts total) Goal 4

Jordan's House to Park: (2 pts)

\(J(8, 9)\) to \(P(2, 1)\)
\(d = \sqrt{(2-8)^2 + (1-9)^2}\)
\(d = \sqrt{(-6)^2 + (-8)^2}\)
\(d = \sqrt{36 + 64} = \sqrt{100} = 10\)
[1 pt setup, 1 pt answer 10]

Alex's House to Park: (2 pts)

\(A(-1, 5)\) to \(P(2, 1)\)
\(d = \sqrt{(2 - (-1))^2 + (1-5)^2}\)
\(d = \sqrt{(3)^2 + (-4)^2}\)
\(d = \sqrt{9 + 16} = \sqrt{25} = 5\)
[1 pt setup, 1 pt answer 5]

Final Comparison Statement: (1 pt)

Alex lives closer (distance of 5 < 10 for Jordan). Stated clearly with mathematical work.

Geometry Quarter 1 Assessment Suite • Test 1 Key Page 2 of 3

Test 1 Key Continued

Question 33 — Goals 2 & 3 — Dog Park Key (5 pts total) Scoring Key

a) Equation & solve \(x\). (2 pts)

\(2(x + 6) + 2(8) = 52\)
\(2x + 12 + 16 = 52\)
\(2x + 28 = 52\)
\(2x = 24 \rightarrow x = 12\)
[1 pt eqn, 1 pt sol]

b) Find Area of Dog Park. (1 pt)

Length = \(x + 6\)
Length = \(12 + 6 = 18\) m
Width = 8 m
Area = \(18 \times 8 = 144 \text{ m}^2\)
[1 pt area with units]

c) Find Landscaping Cost. (2 pts)

Cost = Area \(\times\) $5
Cost = \(144 \times \$5\)
Cost = \(\$720\)

[1 pt setup, 1 pt answer]

Question 34 — Goal 4 — Delivery Trucks Distance Key (5 pts total) Scoring Key

Warehouse W to Customer A: (2 pts)

\(W(1, 2)\) to \(A(4, 10)\)
\(d = \sqrt{(4-1)^2 + (10-2)^2}\)
\(d = \sqrt{3^2 + 8^2}\)
\(d = \sqrt{9 + 64} = \sqrt{73} \approx 8.54\)
[1 pt setup, 1 pt simplified form/dec]

Warehouse W to Customer B: (2 pts)

\(W(1, 2)\) to \(B(9, -4)\)
\(d = \sqrt{(9-1)^2 + (-4-2)^2}\)
\(d = \sqrt{8^2 + (-6)^2}\)
\(d = \sqrt{64 + 36} = \sqrt{100} = 10\)
[1 pt setup, 1 pt answer 10]

Final Comparison Statement: (1 pt)

Customer B is located further from the warehouse (distance of 10 > 8.54 for Customer A). Stated clearly with appropriate comparisons.

Geometry Quarter 1 Assessment Suite • Test 1 Key Page 3 of 3

C \(EF \cong CD\)

D \(EM \cong EF\)

9. Point N is the midpoint of segment GH. If \(GN = 2x\) and \(NH = x + 9\), what is the length of segment \(GH\)?

A 9

B 18

C 36

D 45

10. What is the midpoint of the segment with endpoints A(2, 4) and B(8, 10)?

A (10, 14)

B (5, 7)

C (3, 3)

D (6, 7)

Geometry Quarter 1 Assessment Suite • Test 2 Page 2 of 7

Test 2 • Multiple Choice Continued

11. What is the midpoint of the segment with endpoints C(−6, 3) and D(4, 7)?

A (−1, 5)

B (−5, 2)

C (−1, 2)

D (5, −1)

12. Segment GH is graphed below with endpoints G(2, 5) and H(−4, −1). What is the midpoint of segment GH?

A (−2, 4)

B (3, 2)

C (−1, 3)

D (−1, 2)

13. What is the midpoint of a segment with endpoints P(0, 0) and Q(8, 12)?

A (8, 12)

B (2, 3)

C (4, 6)

D (4, 8)

14. Which of the following correctly names the angle formed by vertex B and sides BA and BC?

A \(\angle BAC\)

B \(\angle ABC\)

C \(\angle ACB\)

D \(\angle CAB\)

15. In the angle \(\angle XYZ\), which point represents the vertex?

A Point X

B Point Z

C Point Y

D No vertex

16. In a diagram, three rays share vertex Q. Which name clearly identifies the marked angle between ray QP and ray QS?

A \(\angle PQS\)

B \(\angle Q\)

C \(\angle S\)

D \(\angle PSQ\)

17. If three rays share a vertex, what is the vertex of angle \(\angle MNO\)?

A Point M

B Point N

C Point O

D No vertex

Geometry Quarter 1 Assessment Suite • Test 2 Page 3 of 7

Test 2 • Multiple Choice Continued

18. Classify the angle shown below:

A Right

B Obtuse

C Straight

D Acute

19. An angle measures 121°. Classify the angle.

A Acute

B Right

C Obtuse

D Straight

20. Which angle measure represents a right angle?

A 45°

B 90°

C 120°

D 180°

21. An angle measures 89°. Classify this angle.

A Acute

B Right

C Obtuse

D Straight

22. Ray QS is inside \(\angle PQR\). If \(m\angle PQS = 32^\circ\) and \(m\angle SQR = 41^\circ\), what is \(m\angle PQR\)?

A 9°

B 41°

C 73°

D 90°

23. In a diagram, \(m\angle ABD = 110^\circ\) and \(m\angle ABC = 45^\circ\) where ray BC is inside \(\angle ABD\). What is \(m\angle CBD\)?

A 65°

B 45°

C 110°

D 155°

24. Angle \(\angle JKL\) is a right angle. Ray KM is inside \(\angle JKL\). If \(m\angle JKM = (2x)^\circ\) and \(m\angle MKL = (x + 15)^\circ\), what is \(x\)?

A 15

B 75

C 30

D 25

Geometry Quarter 1 Assessment Suite • Test 2 Page 4 of 7

Test 2 • Multiple Choice Continued

25. In the figure below, \(m\angle FGH = 124^\circ\), \(m\angle FGJ = (3x + 4)^\circ\), and \(m\angle JGH = (2x)^\circ\) where ray GJ is inside \(\angle FGH\). What is \(m\angle JGH\)?

A 24°

B 48°

C 76°

D 120°

26. Ray BD is inside right angle \(\angle ABC\). If \(m\angle ABD = (3x)^\circ\) and \(m\angle DBC = (x + 10)^\circ\), what is the value of \(x\)?

A 10

B 15

C 20

D 25

27. Ray BD bisects angle \(\angle ABC\). If \(m\angle ABD = 27^\circ\), what is the measure of the entire angle \(\angle ABC\)?

A 13.5°

B 27°

C 54°

D 108°

28. Ray QS bisects angle \(\angle PQR\). If \(m\angle PQS = (4x)^\circ\) and \(m\angle SQR = (2x + 22)^\circ\), what is the value of \(x\)?

A 11

B 22

C 44

D 88

29. Ray KM bisects angle \(\angle JKL\). If the entire angle \(m\angle JKL = 76^\circ\), what is \(m\angle MKL\)?

A 19°

B 76°

C 152°

D 38°

30. Ray BD bisects angle \(\angle ABC\). If \(m\angle ABD = (4x - 2)^\circ\) and \(m\angle DBC = (2x + 10)^\circ\), find \(x\).

A 4

B 6

C 8

D 12

Geometry Quarter 1 Assessment Suite • Test 2 Page 5 of 7

Section 2: Open-Ended Responses (4 Questions • 5 Points Each)

31. Points G, H, J, and K are collinear on the same line segment. If \(GH = x + 4\), \(HJ = 2x\), \(JK = x + 9\), and the entire segment \(GK = 45\):

G H J K x + 4 2x x + 9 GK = 45

a) Write an equation for segment addition and solve for \(x\). (3 pts)

b) Find the length of segment \(HJ\). (2 pts)

32. Ray QS is inside angle \(\angle PQR\). If \(m\angle PQR = 98^\circ\), \(m\angle PQS = (3x + 5)^\circ\), and \(m\angle SQR = (2x + 3)^\circ\):

Q P S R 98° 3x + 5 2x + 3

a) Write an equation using the Angle Addition Postulate and solve for \(x\). (3 pts)

b) Find both angle measures: \(m\angle PQS\) and \(m\angle SQR\). (2 pts)

Geometry Quarter 1 Assessment Suite • Test 2 Page 6 of 7

Test 2 • Open-Ended Continued

33. Ray BD bisects angle \(\angle ABC\). If \(m\angle ABD = (5x - 6)^\circ\) and \(m\angle DBC = (3x + 12)^\circ\):

B A D C 5x − 6 3x + 12

a) Write an equation and solve for \(x\). (3 pts)

b) Find the measure of the entire angle, \(m\angle ABC\). (2 pts)

34. Segment AB has endpoints A(−4, 8) and B(2, −2). Point M is the midpoint of segment AB.

A(-4,8) B(2,-2)

a) Use the midpoint formula to find the coordinates of point M. Show your work. (3 pts)

b) In one sentence, explain what it means for M to be the midpoint of segment AB. (2 pts)

Geometry Quarter 1 Assessment Suite • Test 2 Page 7 of 7

Q25. B Goal 10

Q26. C Goal 10

Q27. C Goal 11

Q28. A Goal 11

Q29. D Goal 11

Q30. B Goal 11

Q31 — Segment Addition Key Goal 5

a) Write equation and solve for \(x\): (3 pts)

\(GH + HJ + JK = GK\)
\((x + 4) + 2x + (x + 9) = 45\)
\(4x + 13 = 45 \rightarrow 4x = 32 \rightarrow x = 8\)
[1 pt equation setup, 1 pt work, 1 pt solution]

b) Find HJ length: (2 pts)

\(HJ = 2x = 2(8) = 16\)
Check: \(12 + 16 + 17 = 45\) ✓
[1 pt substitution, 1 pt correct answer]

Q32 — Angle Addition Postulate Key (5 pts total) Goal 10

a) Write equation and solve: (3 pts)

\(m\angle PQS + m\angle SQR = m\angle PQR\)
\((3x + 5) + (2x + 3) = 98\)
\(5x + 8 = 98\)
\(5x = 90 \rightarrow x = 18\)
[1 pt equation, 1 pt steps, 1 pt solution]

b) Find both angle measures: (2 pts)

\(m\angle PQS = 3(18) + 5 = 59^\circ\)
\(m\angle SQR = 2(18) + 3 = 39^\circ\)
Check: \(59^\circ + 39^\circ = 98^\circ\) ✓
[1 pt for each correct angle measure]

Geometry Quarter 1 Assessment Suite • Test 2 Key Page 2 of 3

Test 2 Key Continued

Question 33 — Goal 11 — Angle Bisector Key (5 pts total) Scoring Key

a) Write an equation and solve for \(x\). (3 pts)

Since BD bisects \(\angle ABC\):
\(5x - 6 = 3x + 12\)
Subtract \(3x\): \(2x - 6 = 12\)
Add 6: \(2x = 18\)
Divide by 2: \(x = 9\)
[1 pt equation, 1 pt work steps, 1 pt solution]

b) Find measure of entire \(\angle ABC\). (2 pts)

Each half angle:
\(m\angle ABD = 5(9) - 6 = 39^\circ\)
\(m\angle DBC = 3(9) + 12 = 39^\circ\) ✓
Entire angle:
\(m\angle ABC = m\angle ABD + m\angle DBC\)
\(m\angle ABC = 39^\circ + 39^\circ = 78^\circ\)
[1 pt half measurement, 1 pt correct entire angle]

Question 34 — Goals 6 & 7 — Midpoint Coordinate Key (5 pts total) Scoring Key

a) Find midpoint coordinate: (3 pts)

Endpoints: \(A(-4, 8)\) and \(B(2, -2)\)
\(M = \left( \frac{-4 + 2}{2}, \frac{8 + (-2)}{2} \right)\)
\(M = \left( \frac{-2}{2}, \frac{6}{2} \right)\)
\(M = (-1, 3)\)
[1 pt formula/setup, 1 pt step work, 1 pt final coordinates]

b) Midpoint explanation sentence: (2 pts)

Accept any reasonable conceptual statement, such as:
• Point M is exactly halfway between endpoint A and endpoint B.
• Point M splits segment AB into two congruent pieces such that \(AM = MB\).

[2 pts clear conceptual sentence, 1 pt if partially complete]

Geometry Quarter 1 Assessment Suite • Test 2 Key Page 3 of 3

20 30 50 65

A Cluster

B Gap

C Outlier

D Mode

8. A distribution has two separate “humps” (peaks) when graphed. What term describes this feature?

A Bimodal

B Skewed

C Uniform

D Symmetric

Statistics Quarter 1 Assessment Suite • Quiz 1 Page 2 of 5

Quiz 1 • Multiple Choice Continued

9. A dataset is shaped like a bell where the left side and right side are mirror images. What shape is this?

A Skewed left

B Skewed right

C Symmetric

D Bimodal

10. A gap in a dot plot refers to:

A A cluster of many data points.

B An area with no data points between values.

C The highest data point in the display.

D The average height of all columns.

Questions 11–13 refer to the following sorted data set:

4, 7, 7, 9, 12, 15, 20

11. Find the median of the data set.

A 7

B 9

C 12

D 10.75

12. Find the mode of the data set.

A 4

B 7

C 9

D No mode

Statistics Quarter 1 Assessment Suite • Quiz 1 Page 3 of 5

Quiz 1 • Multiple Choice Continued

13. Find the range of the data set: 4, 7, 7, 9, 12, 15, 20.

A 7

B 9

C 16

D 20

14. Find the range of the following data set: 10, 15, 20, 25, 30.

A 10

B 15

C 20

D 30

15. Find the median of the following sorted data set: 5, 8, 12, 15.

A 8

B 10

C 12

D 15

Statistics Quarter 1 Assessment Suite • Quiz 1 Page 4 of 5

Section 2: Open-Ended Responses (2 Questions • 5 Points Each)

16. The data set below shows the number of books read by 9 students over the summer.

12, 15, 18, 18, 21, 24, 27, 30, 33

a) Find the median and the mode of the data set. (2 pts)

b) Find the range of the data set. (1 pt)

c) Calculate the mean (average) of the data set. Show your work. (2 pts)

17. A small group of 7 families recorded the number of hours they spent reading together in a month:

10, 14, 14, 16, 20, 22, 28

a) Find the median and the mode of the reading hours. (2 pts)

b) Find the range of the reading hours. (1 pt)

c) Calculate the mean (average) of the reading hours. Show your work. (2 pts)

Statistics Quarter 1 Assessment Suite • Quiz 1 Page 5 of 5

b) Find the range of the reading hours. (1 pt)

Range = Max − Min = 28 − 10 = 18
[1 pt correct calculation setup or answer of 18]

c) Calculate the mean (average) of the reading hours. (2 pts)

Sum = 10 + 14 + 14 + 16 + 20 + 22 + 28 = 124
Mean = 124 / 7 ≈ 17.71 hours
[1 pt correct addition/division setup, 1 pt correct answer 17.71 (or rounded 17.7)]

Statistics Quarter 1 Assessment Suite • Quiz 1 Answer Key Page 2 of 2

A Increase

B Decrease

C Stay same

D Cannot tell

9. Which data set would have the LARGER standard deviation?
   Set A: 10, 10, 10, 10, 10  •  Set B: 2, 6, 10, 14, 18

A Set A

B Set B

C They are equal

D Cannot tell

10. A data set has a mean of 50 and a standard deviation of 5. Which value is more unusual (further away from the mean)?

A 40

B 58

C Equally unusual

D Cannot tell

11. What does a standard deviation of 0 tell you about a data set?

A All the data values are identical.

B The data is perfectly symmetric.

C The data has absolutely no outliers.

D The mean is equal to 0.

12. Generally, standard deviation is a direct mathematical measure of:

A Center

B Spread/variation

C Shape

D Sample size

Statistics Quarter 1 Assessment Suite • Quiz 2 Page 3 of 5

Quiz 2 • Multiple Choice Continued

13. In a right-skewed (positively skewed) distribution, which measure of center is typically LARGER?

A Mean

B Median

C Mode

D They are equal

14. A data set has a mean of 45 and a median of 60. What does this suggest about the shape of the distribution?

A Skewed right

B Skewed left

C Symmetric

D Uniform

15. Why is the median often preferred over the mean when a data set contains major outliers?

A The median is always larger than the mean.

B The mean is much more difficult to calculate.

C The median is resistant (not affected heavily) by outliers.

D The median uses every single value in the calculations.

Statistics Quarter 1 Assessment Suite • Quiz 2 Page 4 of 5

Section 2: Open-Ended Responses (2 Questions • 5 Points Each)

16. Construct a boxplot representing the books read over the summer. The five-number summary is:
    Min = 12  •  Q1 = 16.5  •  Median = 21  •  Q3 = 28.5  •  Max = 33

a) Construct a correct boxplot on the number line below: (2 pts)

0 6 12 18 24 30 36

b) Clearly label where the median line is inside your boxplot. (1 pt)

c) Calculate the Interquartile Range (IQR) for this data set. (2 pts)

17. The data set below shows the ages (in years) of 8 dogs at an animal shelter:

5, 8, 9, 10, 11, 12, 14, 34

a) Find the values of \(Q_1\) and \(Q_3\). (1 pt)

b) Calculate the IQR and find the Upper Fence value (\(Q_3 + 1.5 \times IQR\)). (2 pts)

c) Is the dog age of 34 an outlier? Explain your reasoning using the upper fence. (2 pts)

Statistics Quarter 1 Assessment Suite • Quiz 2 Page 5 of 5

Lower half: 5, 8, 9, 10 → \(Q_1 = (8 + 9) / 2 = 8.5\)
Upper half: 11, 12, 14, 34 → \(Q_3 = (12 + 14) / 2 = 13\)
[1 pt for both correct quartiles: \(Q_1 = 8.5\) and \(Q_3 = 13\)]

b) Calculate the IQR and the Upper Fence. (2 pts)

\(IQR = Q_3 - Q_1 = 13 - 8.5 = 4.5\)
Upper Fence = \(Q_3 + 1.5(IQR) = 13 + 1.5(4.5) = 13 + 6.75 = 19.75\)
[1 pt correct IQR of 4.5, 1 pt correct upper fence of 19.75]

c) Is 34 an outlier? Explain using the upper fence. (2 pts)

Yes, 34 is an outlier.
Explanation: Since the age of 34 is greater than the upper fence value of 19.75 (\(34 > 19.75\)), it is mathematically classified as an outlier.
[1 pt correct “Yes”, 1 pt correct mathematical comparison to 19.75]

Statistics Quarter 1 Assessment Suite • Quiz 2 Answer Key Page 2 of 2

A 3

B 6

C 9

D 20

8. On a standard frequency histogram, the height of each vertical bar represents:

A The raw data value itself.

B The range of the values.

C The frequency (count) of values in that interval.

D The mean of the entire data set.

9. A dataset has a long tail extending to the left, while most of the values are clustered on the right side. What is the shape of this distribution?

A Skewed right

B Skewed left

C Symmetric

D Uniform

10. In a dot plot, most values cluster between 20 and 30, but there is a single data value at 65 that is far from the rest. What term describes the value of 65?

A Cluster

B Gap

C Outlier

D Mode

Geometry Quarter 1 Assessment Suite • Test 1 Page 2 of 7

Test 1 • Multiple Choice Continued

11. A distribution has two separate “humps” (peaks) when graphed. What term describes this feature?

A Bimodal

B Skewed

C Uniform

D Symmetric

12. A dataset is shaped like a bell where the left side and right side are mirror images. What shape is this?

A Skewed left

B Skewed right

C Symmetric

D Bimodal

13. A dot plot has many points from 10 to 15, then no points between 15 and 35, then a point at 35. The space between 15 and 35 is called:

A Outlier

B Gap

C Peak

D Cluster

14. A distribution has a long tail extending to the right. What is its shape?

A Skewed right

B Skewed left

C Symmetric

D Uniform

15. In a uniform distribution, the heights of all the bars on a histogram are:

A Heavily pulled to the left.

B Heavily pulled to the right.

C Approximately equal across all values.

D Showing two distinct and equal peaks.

Questions 16–18 refer to the following sorted data set:

4, 7, 7, 9, 12, 15, 20

16. Find the median of the data set.

A 7

B 9

C 12

D 10.75

Geometry Quarter 1 Assessment Suite • Test 1 Page 3 of 7

Test 1 • Multiple Choice Continued

17. Find the mode of the data set: 4, 7, 7, 9, 12, 15, 20.

A 4

B 7

C 9

D No mode

18. Find the range of the data set: 4, 7, 7, 9, 12, 15, 20.

A 7

B 9

C 16

D 20

19. Find the range of the following data set: 10, 15, 20, 25, 30.

A 10

B 15

C 20

D 30

20. Find the median of the following sorted data set: 5, 8, 12, 15.

A 8

B 10

C 12

D 15

21. Find the mode of the following data set: 2, 3, 3, 4, 5.

A 2

B 3

C 4

D 5

22. Which equation correctly calculates the range of a numeric dataset?

A \(\text{Range} = \text{Median} - \text{Mean}\)

B \(\text{Range} = \text{Maximum} - \text{Minimum}\)

C \(\text{Range} = Q_3 - Q_1\)

D \(\text{Range} = \frac{\text{Sum of values}}{\text{Total count}}\)

Questions 23–27 refer to the following sorted data set of 9 test scores:

2, 5, 6, 9, 12, 15, 18, 20, 23

23. What is the minimum value of this data set?

A 2

B 5.5

C 12

D 23

Geometry Quarter 1 Assessment Suite • Test 1 Page 4 of 7

Test 1 • Multiple Choice Continued

24. What is \(Q_1\) (the first quartile) of this data set?

A 5

B 5.5

C 6

D 9

25. What is \(Q_3\) (the third quartile) of this data set?

A 18

B 19

C 20

D 23

26. What is the maximum value of this data set?

A 12

B 18

C 20

D 23

27. What is the median value of this data set?

A 12

B 9

C 15

D 6

28. The five-number summary contains all of the following statistics EXCEPT:

A Mean

B Median

C Q1

D Minimum

29. For the sorted data set: 3, 5, 8, 10, 12, what is the value of \(Q_1\)?

A 3

B 4

C 5

D 8

30. For the same sorted data set: 3, 5, 8, 10, 12, what is the value of \(Q_3\)?

A 8

B 10

C 11

D 12

Geometry Quarter 1 Assessment Suite • Test 1 Page 5 of 7

Section 2: Open-Ended Responses (4 Questions • 5 Points Each)

31. The data set below shows the number of books read by 9 students over the summer.

12, 15, 18, 18, 21, 24, 27, 30, 33

a) Find the median and the mode of the data set. (2 pts)

b) Find the range of the data set. (1 pt)

c) Determine \(Q_1\) and \(Q_3\) of the data set. (2 pts)

32. The data set below shows the exam preparation hours of 9 high school students:

5, 8, 10, 10, 12, 14, 16, 18, 22

a) Find the median and the mode of the preparation hours. (2 pts)

b) Find the range of the preparation hours. (1 pt)

c) Find the \(Q_1\) and \(Q_3\) quartile values. (2 pts)

Geometry Quarter 1 Assessment Suite • Test 1 Page 6 of 7

Test 1 • Open-Ended Continued

33. The mathematics test scores of 10 students are recorded below:

62, 65, 71, 74, 78, 80, 83, 83, 85, 92

a) Construct a stemplot to represent these test scores. Include a clear key! (3 pts)

b) Find the range of the scores. (1 pt)

c) Identify the mode of the scores. (1 pt)

34. Two basketball players scored the following points in their last 5 games:

Player A: 10, 12, 15, 18, 20  •  Player B: 5, 15, 15, 15, 25

a) Calculate the Mean score for both: (2 pts)

b) State the Median score for both: (1 pt)

c) Which player is more consistent? Explain using the range. (2 pts)

Geometry Quarter 1 Assessment Suite • Test 1 Page 7 of 7

b) Find Range: (1 pt)

Range = 33 − 12 = 21
[1 pt correct range]

c) Find Q1 and Q3: (2 pts)

Lower half: 12, 15, 18, 18 → \(Q_1 = 16.5\)
Upper half: 24, 27, 30, 33 → \(Q_3 = 28.5\)
[1 pt \(Q_1\), 1 pt \(Q_3\)]

Q32 — Exam Preparation Hours Key (5 pts total) Goals 3, 4

a) Find the median and the mode: (2 pts)

Ordered: 5, 8, 10, 10, 12, 14, 16, 18, 22
Median = 12 (middle score)
Mode = 10 (appears twice)
[1 pt median 12, 1 pt mode 10]

b) Find range: (1 pt)

Range = 22 − 5 = 17
[1 pt range 17]

c) Find Q1 and Q3: (2 pts)

Lower half: 5, 8, 10, 10 → \(Q_1 = 9\)
Upper half: 14, 16, 18, 22 → \(Q_3 = 17\)
[1 pt \(Q_1 = 9\), 1 pt \(Q_3 = 17\)]

Statistics Quarter 1 Assessment Suite • Test 1 Key Page 2 of 3

Test 1 Key Continued

Question 33 — Goals 1 & 3 — Score Stemplot • Key (5 pts total) Scoring Key

a) Stemplot Construction: (3 pts)

6 | 2 5
7 | 1 4 8
8 | 0 3 3 5
9 | 2
Key: 6 | 2 means 62 scores
[1.5 pts correct sorting stems and leaves, 1.5 pts key provided and correct]

b) Find Range: (1 pt)

Range = 92 − 62 = 30
[1 pt correct 30]

c) Determine Mode: (1 pt)

Mode = 83 (appears twice)
[1 pt correct 83]

Question 34 — Goals 3 & 4 — Consistency Comparison (5 pts total) Scoring Key

a) Calculate Means: (2 pts)

Player A mean:
\(\frac{10+12+15+18+20}{5} = \frac{75}{5} = 15\)
Player B mean:
\(\frac{5+15+15+15+25}{5} = \frac{75}{5} = 15\)
[1 pt player A, 1 pt player B]

b) Find Medians: (1 pt)

Player A median = 15
Player B median = 15

Both medians are equal.
[1 pt for both correct medians]

c) Which player is more consistent? Explain using range: (2 pts)

Player A range: \(20 - 10 = 10\) points.  •  Player B range: \(25 - 5 = 20\) points.
Player A is more consistent because they have a smaller range (10 points vs 20 points), meaning their scores are less spread out and closer together.
[1 pt correct player A choice, 1 pt math justification using calculated range comparison]

Statistics Quarter 1 Assessment Suite • Test 1 Key Page 3 of 3

A Increase

B Decrease

C Stay same

D Cannot tell

9. Which data set would have the LARGER standard deviation?
   Set A: 10, 10, 10, 10, 10  •  Set B: 2, 6, 10, 14, 18

A Set A

B Set B

C They are equal

D Cannot tell

10. A data set has a mean of 50 and a standard deviation of 5. Which value is more unusual (further away from the mean)?

A 40

B 58

C Equally unusual

D Cannot tell

Statistics Quarter 1 Assessment Suite • Test 2 Page 2 of 7

Test 2 • Multiple Choice Continued

11. What does a standard deviation of 0 tell you about a data set?

A All the data values are identical.

B The data is perfectly symmetric.

C The data has absolutely no outliers.

D The mean is equal to 0.

12. Generally, standard deviation is a direct mathematical measure of:

A Center

B Spread/variation

C Shape

D Sample size

13. In a right-skewed (positively skewed) distribution, which measure of center is typically LARGER?

A Mean

B Median

C Mode

D They are equal

14. A data set has a mean of 45 and a median of 60. What does this suggest about the shape of the distribution?

A Skewed right

B Skewed left

C Symmetric

D Uniform

15. Why is the median often preferred over the mean when a data set contains major outliers?

A The median is always larger than the mean.

B The mean is much more difficult to calculate.

C The median is resistant (not affected heavily) by outliers.

D The median uses every single value in the calculations.

16. If a very high outlier data score is added to a symmetric dataset, which summary statistic will change the most?

A Median

B Mode

C Mean

D None of these

Statistics Quarter 1 Assessment Suite • Test 2 Page 3 of 7

Test 2 • Multiple Choice Continued

17. Which of the following is NOT a feature typically used to describe and compare two different distributions?

A Shape

B Center

C Spread

D Total digits

18. Two classes took the same test. Class 1: median = 78, IQR = 10. Class 2: median = 78, IQR = 25. Which class has more consistent (less variable) scores?

A Class 1

B Class 2

C They are equal

D Cannot tell

19. Data Set A has a mean of 80 and standard deviation of 4. Data Set B has a mean of 80 and standard deviation of 12. Which statement is true?

A Data Set A has more variability than Data Set B.

B Data Set B has more variability than Data Set A.

C Both data sets have the exact same variability.

D The datasets cannot be compared mathematically.

20. When comparing two boxplots visually, which measure of center is easiest to compare directly?

A Mean

B Median

C Mode

D SD

21. A data set has a mean of 70 and a standard deviation of 5. What is the z-score for a value of 80?

A 0.5

B 2

C 10

D 50

22. A data set has a mean of 100 and a standard deviation of 15. What is the z-score for a value of 85?

A −1

B −15

C 1

D 15

Statistics Quarter 1 Assessment Suite • Test 2 Page 3 of 7

Test 2 • Multiple Choice Continued

23. A value has a z-score of 1.5 in a distribution with a mean of 60 and standard deviation of 8. What is the actual value?

A 61.5

B 68

C 72

D 90

24. A value has a z-score of −2 in a distribution with a mean of 50 and standard deviation of 4. What is the actual value?

A 42

B 46

C 48

D 58

25. A calculated z-score of exactly 0 tells us that the corresponding raw data value is:

A Equal to the median value.

B Exactly equal to the mean value.

C The maximum score in the set.

D A mathematically extreme outlier.

Questions 26–28 refer to the following scenario:

On a mathematics exam, the class mean was 75 with standard deviation 5. On a science exam, the mean was 70 with standard deviation 4. Maria scored 85 on mathematics and 78 on science.

26. Calculate Maria’s z-score on the mathematics test.

A 1

B 2

C 5

D 10

Statistics Quarter 1 Assessment Suite • Test 2 Page 4 of 7

Test 2 • Multiple Choice Continued

27. Calculate Maria’s z-score on the science test.

A 1

B 2

C 8

D 78

28. Based on the z-scores above, on which test did Maria perform relatively better compared to her class peers?

A Mathematics Exam

B Science Exam

C She performed equally well on both.

D Cannot be determined mathematically.

29. John scored 90 on a test with mean 80 and SD 5. Mike scored 85 on a test with mean 70 and SD 10. Who performed relatively better?

A John (z-score of 2.0 vs 1.5)

B Mike (z-score of 1.5 vs 2.0)

C They performed equally well.

D Cannot tell without more statistics.

30. A negative z-score mathematically indicates that the corresponding raw score value is:

A Below the mean

B Above the mean

C An outlier

D Equal to mean

Statistics Quarter 1 Assessment Suite • Test 2 Page 5 of 7

Section 2: Open-Ended Responses (4 Questions • 5 Points Each)

31. Construct a boxplot representing the books read over the summer. The five-number summary is:
    Min = 12  •  Q1 = 16.5  •  Median = 21  •  Q3 = 28.5  •  Max = 33

a) Construct a correct boxplot on the number line below: (2 pts)

0 6 12 18 24 30 36

b) Clearly label the median line inside your boxplot. (1 pt)

c) Calculate the Interquartile Range (IQR). (2 pts)

32. The data set below shows the ages (in years) of 8 dogs at an animal shelter:

5, 8, 9, 10, 11, 12, 14, 34

a) Find the values of \(Q_1\) and \(Q_3\). (1 pt)

b) Calculate the IQR and find the Upper Fence value (\(Q_3 + 1.5 \times IQR\)). (2 pts)

c) Is the dog age of 34 an outlier? Explain your reasoning using the upper fence. (2 pts)

Statistics Quarter 1 Assessment Suite • Test 2 Page 6 of 7

Test 2 • Open-Ended Continued

33. Standard Deviation & Skewness analysis.

a) Two vending machines fill bags of chips. Machine A has a mean weight of 8 oz with standard deviation 0.1 oz. Machine B has a mean weight of 8 oz with standard deviation 0.5 oz. Which machine is more consistent? Explain your reasoning. (2 pts)

b) Explain in one sentence what standard deviation represents or measures in statistics. (1 pt)

c) A set of quiz scores has a mean of 72 and a median of 85. Based on this relationship, is the distribution skewed left, skewed right, or symmetric? Justify. (2 pts)

34. Jamal's height is 70 inches. Heights of students in his grade have a mean of 66 inches with standard deviation 2.5 inches. Diego's height is 74 inches. Heights of students in his older grade have a mean of 69 inches with standard deviation 3 inches.

Determine who is relatively taller inside their own grades. (5 pts total)

a) Calculate Jamal's z-score: (2 pts)

b) Calculate Diego's z-score: (2 pts)

c) Who is relatively taller? Justify your answer using the z-scores you calculated: (1 pt)

Geometry Quarter 1 Assessment Suite • Test 2 Page 7 of 7

Q25. B Goal 10

Q26. B Goal 11

Q27. B Goal 11

Q28. C Goal 11

Q29. A Goal 11

Q30. A Goal 11

Q31 — Summer Books Boxplot Key Goal 5

a) Construct Boxplot: (2 pts)

• Box drawn from \(16.5\) (\(Q_1\)) to \(28.5\) (\(Q_3\)). [1 pt]
• Whiskers from \(12\) (Min) to \(16.5\); from \(28.5\) to \(33\) (Max). [1 pt]

b) Median Label: (1 pt)

Vertical line labeled inside box at the value of \(21\). [1 pt]

c) Calculate IQR: (2 pts)

\(IQR = Q_3 - Q_1 = 28.5 - 16.5 = 12\)
[1 pt setup, 1 pt answer 12]

Q32 — Shelter Dogs Outlier Key (5 pts total) Goal 6

a) Find \(Q_1\) and \(Q_3\): (1 pt)

Lower: 5, 8, 9, 10 → \(Q_1 = (8+9)/2 = 8.5\)
Upper: 11, 12, 14, 34 → \(Q_3 = (12+14)/2 = 13\)
[1 pt for both correct quartiles]

b) Calculate IQR & Fence: (2 pts)

\(IQR = 13 - 8.5 = 4.5\)
Upper Fence = \(13 + 1.5(4.5) = 19.75\)
[1 pt IQR, 1 pt Upper Fence]

c) Outlier decision & why: (2 pts)

Yes, 34 is an outlier. Since \(34 > 19.75\), the score value is outside the fence limits.
[1 pt Yes, 1 pt comparison work]

Statistics Quarter 1 Assessment Suite • Test 2 Key Page 2 of 3

Test 2 Key Continued

Question 33 — Goals 7 & 8 — SD and Skewness Analysis Key (5 pts total) Scoring Key

a) Which machine is more consistent? Explain: (2 pts)

Machine A is more consistent because it has a smaller standard deviation (0.1 oz vs 0.5 oz for Machine B), which means the bag weights vary much less and are closer to the 8 oz target.
[1 pt Machine A, 1 pt clear reasoning using smaller standard deviation]

b) What does SD measure? (1 pt)

Accept any statement showing it measures the typical or average distance of values from the mean. [1 pt]

c) Find and justify skewness shape: (2 pts)

Skewed left.
Justification: Since the Mean (72) is less than the Median (85), the mean is pulled down by a low tail or outliers.
[1 pt skewed left, 1 pt correct mean vs median justification]

Question 34 — Goals 10 & 11 — Jamal & Diego Z-Score Key (5 pts total) Scoring Key

a) Calculate Jamal's z-score: (2 pts)

\(z_J = \frac{70 - 66}{2.5}\)
\(z_J = \frac{4}{2.5} = 1.6\)
[1 pt correct setup, 1 pt correct answer 1.6]

b) Calculate Diego's z-score: (2 pts)

\(z_D = \frac{74 - 69}{3}\)
\(z_D = \frac{5}{3} \approx 1.67\)
[1 pt correct setup, 1 pt correct answer 1.67]

c) Who is relatively taller and why? (1 pt)

Diego is relatively taller because his z-score (1.67) is higher than Jamal's z-score (1.6), indicating Diego is further above his peer group's mean in terms of standard deviations. [1 pt]

Statistics Quarter 1 Assessment Suite • Test 2 Key Page 3 of 3