Answer Keys: Data Displays

Student Concept Worksheet Answers

1

a) 6, b) 20, c) 10-19

Reading histogram: a) The 10-19 bar shows 6. b) Total = 4+6+3+5+2 = 20 people. c) The tallest bar is at 10-19 with 6 people.

2

Min=12, Q1=16.5, Median=22, Q3=29, Max=35, IQR=12.5

Data (9 values): 12, 15, 18, 20, 22, 25, 28, 30, 35. Median = 22 (5th value). Lower half: 12, 15, 18, 20. Q1 = (15+18)/2 = 16.5. Upper half: 25, 28, 30, 35. Q3 = (28+30)/2 = 29. IQR = 29-16.5 = 12.5

3

a) 62, b) 75, c) 23, d) 13, e) 25%

Reading box plot: a) Min = 62 (left whisker end). b) Median = 75 (line in box). c) Range = 85-62 = 23. d) IQR = 82-69 = 13. e) 25% scored above Q3 (above 82), so approximately 25% scored above 75 (above the median is 50%).

4

a) Box plot, b) Histogram

a) Box plots are great for comparing two groups side-by-side - you can easily see differences in medians and spread. b) Histograms show frequency in each range, perfect for seeing how many fall in each grade category.

Practice Worksheet Answers

Part A: Reading Histograms

1

a) 8, b) 22, c) 6-8 hours, d) 8

a) Bar at 6-8 shows 8 students. b) Total = 3+5+8+4+2 = 22. c) The 6-8 interval has the tallest bar (8). d) 0-2 and 3-5 combined = 3+5 = 8 students spent less than 6 hours.

2

a) 70-74, b) 13, c) Approximately symmetric (slight skew)

a) The 70-74 bar is tallest (9 days). b) 75-79 (7) + 80-84 (6) = 13 days were 75 or higher. c) The distribution is roughly symmetric with a slight peak in the middle.

Part B: Reading Box Plots

3

Min=24, Q1=28, Median=33, Q3=38, Max=43, IQR=10

Reading from the box plot scale. IQR = 38-28 = 10. 50% of employees are between 28 and 38 (the middle 50% = the box).

4

a) 26, b) 44, c) 25%, d) 18 and 35

a) Median line is at 26. b) Range = 48-4 = 44. c) 25% is below Q1 (18 or less). d) The box spans Q1 (18) to Q3 (35).

Part C: Finding Five-Number Summary

5

Ordered: 68, 70, 72, 75, 78, 82, 85, 88, 90, 95

Min=68, Q1=72, Median=80, Q3=88, Max=95, IQR=16, Range=27

10 values, so median = (78+82)/2 = 80. Lower half: 68, 70, 72, 75, 78. Q1 = 72. Upper half: 82, 85, 88, 90, 95. Q3 = 88. IQR = 88-72 = 16. Range = 95-68 = 27.

6

Ordered: 6200, 7500, 8500, 8800, 9800, 10500, 11000, 12000

Min=6200, Q1=8000, Median=9300, Q3=10750, Max=12000, IQR=2750

8 values. Median = (8800+9800)/2 = 9300. Q1 = (7500+8500)/2 = 8000. Q3 = (10500+11000)/2 = 10750. IQR = 10750-8000 = 2750.

Part D: Comparing Box Plots

7

a) Class A, b) Class A, c) Class B, d) Class B

Reading both box plots: a) Class A median is higher (around 75 vs 73). b) Class A has a wider box (larger IQR). c) Class B has longer whiskers (larger range). d) Class B is more consistent (smaller IQR means middle 50% is closer together).

Part E: Real-World Applications

8

Ordered: 1.8, 2.2, 2.5, 2.7, 2.9, 3.0, 3.2, 3.5, 3.8, 4.0, 4.5, 5.1

Min=1.8, Q1=2.6, Median=3.1, Q3=3.9, Max=5.1, IQR=1.3

12 values. Median = (3.0+3.2)/2 = 3.1. Q1 = (2.5+2.7)/2 = 2.6. Q3 = (3.8+4.0)/2 = 3.9. 50% of fish (between Q1 and Q3) weighed between 2.6 and 3.9 pounds.

9

a) 12, b) 26, c) about 62%, d) Skewed right

a) 3-5 hours interval has 12 students. b) 4+12+8+2 = 26 students. c) Less than 6 hours = 4+12 = 16 out of 26 = 61.5% (about 62%). d) Most students are in lower intervals, with fewer in higher intervals = skewed right.

Challenge Answers:

#10: 10 data points are between 25 and 50. The box contains the middle 50% of data, so 50% of 20 = 10 data points.

#11: Many answers possible. Example: 4, 6, 7, 8, 9, 10, 12, 14, 16. Mean = 86/9 = 9.56 (need to adjust). Better: 4, 7, 8, 9, 9, 10, 12, 13, 16. Sum = 88, not 90. Final: 4, 6, 8, 9, 9, 11, 12, 14, 17 doesn't work either. Correct answer: 4, 7, 8, 9, 9, 11, 12, 14, 16 (sum=90, median=9, range=12).

FAST Practice Quiz Answers

1

B) 20

Add all frequencies: 4+7+5+3+1 = 20 students surveyed.

2

B) 20

IQR = Q3 - Q1 = 85 - 65 = 20

3

B) 50%

The median is 8. 50% of students are above the median. So 50% played more than 8 hours.

4

Select: ALL statements are TRUE

Data: 10, 15, 18, 22, 25, 28, 32, 35, 40 (9 values)
Median = 25 (5th value) - TRUE
Q1 = (15+18)/2 = 16.5 - TRUE
Q3 = (32+35)/2 = 33.5 - TRUE
IQR = 33.5-16.5 = 17 - TRUE
Range = 40-10 = 30 - TRUE

5

B) Skewed left (toward lower values)

When most data is at the higher end with a "tail" extending toward lower values, the distribution is skewed left. The peak is on the right with fewer values trailing to the left.

6

C) Class B has a larger range than Class A

Class A: Range = 90-60 = 30. Class B: Range = 98-55 = 43. Class B has a larger range. Also, Class B has a higher median than Class A, and Class B has a larger IQR than Class A.

FAST Quiz Scoring Guide

Score	Interpretation	Recommended Action
6/6	Mastery	Ready for comparing multiple data sets and making predictions based on data displays.
4-5/6	Approaching Mastery	Review specific concepts: calculating IQR, interpreting percentages from box plots, or reading histogram frequencies.
2-3/6	Developing	Focus on five-number summary. Use physical number cards to practice finding quartiles. Review histogram bar reading.
0-1/6	Needs Intervention	Start with ordering data and finding median. Build understanding of median before introducing quartiles and box plots.

Common Errors to Address:

Forgetting to order data: Must order from least to greatest before finding median and quartiles
Confusing median with mean: The line in a box plot is always the median, not the mean
Box contains all data: The box only contains the middle 50%, whiskers show min/max
Histogram vs bar graph: Histogram bars touch (continuous data), bar graph bars don't (categories)
IQR calculation: IQR = Q3 - Q1, not Q3 - Q1 - median

ANSWER KEYS - Teacher Use Only

Challenge Answers:

Common Errors to Address: