Practice worksheet for creating and interpreting histograms from given data sets.

Here are the solutions to the problems on the worksheet.

Part 1: Birth Years at Parkway Elementary School

Step 1: Fill in the Frequency Table
We need to count how many birth years fall into each range (decade).

* 1990s (1990–1999):
* The years are: 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999.
* Count: 10 students.

* 2000s (2000–2009):
* The years are: 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009.
* Count: 10 students.

* 2010s (2010–2019):
* The years are: 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019.
* Count: 10 students.

* 2020s (2020–2029):
* The years are: 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029.
* Count: 10 students.

Frequency Table:
| Year range | Frequency |
| :--- | :--- |
| 1990s | 10 |
| 2000s | 10 |
| 2010s | 10 |
| 2020s | 10 |

Step 2: Create a Histogram
To draw the histogram based on the table above:
* Draw bars for each decade (1990s, 2000s, 2010s, 2020s).
* Make every bar reach the height of 10 on the vertical axis (Frequency). All bars will be the same height.

Step 3: Answer the Questions
* What decade was the most-often occurring in this set of data?
Since every decade has exactly 10 students, they all occur equally often. There is no single "most-often" decade; it is a tie between all of them.
* True or False: The teachers who teach these kids were not born in 40 years.
This statement is False. Teachers are adults. Even the youngest teachers were likely born in the 1990s or early 2000s. Since the list includes birth years from the 1990s and 2000s, it is very possible (and likely) that some teachers were born in those years. Saying they were *not* born in those years is incorrect.

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Part 2: High School Track Team Mile Times

Step 1: Fill in the Frequency Table
Let's sort the times into the correct groups.
The data points are:
7.55, 7.70, 8.35, 8.95, 6.12, 7.45, 7.00, 6.90, 5.96, 10.10, 7.35, 7.10, 9.35, 9.25, 6.85, 7.98, 8.21, 6.52

* 5.55 – 6.54:
* Numbers: 6.12, 5.96, 6.52
* Count: 3

* 6.55 – 7.54:
* Numbers: 7.55 (No, too high), 7.45, 7.00, 6.90, 7.35, 7.10, 6.85
* Wait, let's look closer at 7.55. It goes in the next group.
* Numbers in this group: 7.45, 7.00, 6.90, 7.35, 7.10, 6.85
* Count: 6

* 7.55 – 8.54:
* Numbers: 7.55, 8.35, 7.98, 8.21
* Count: 4

* 8.55 – 9.54:
* Numbers: 8.95, 9.35, 9.25
* Count: 3

* 9.55 – 10.54:
* Numbers: 10.10
* Count: 1

*(Check: 3 + 6 + 4 + 3 + 1 = 17 numbers. Let me re-count the original list.
1. 7.55, 2. 7.70, 3. 8.35, 4. 8.95, 5. 6.12, 6. 7.45, 7. 7.00, 8. 6.90, 9. 5.96, 10. 10.10, 11. 7.35, 12. 7.10, 13. 9.35, 14. 9.25, 15. 6.85, 16. 7.98, 17. 8.21, 18. 6.52.
There are 18 numbers. I missed one in my first pass. Let's re-sort carefully.)*

Re-sorting all 18 numbers:
1. 5.55 – 6.54: 5.96, 6.12, 6.52 → Count: 3
2. 6.55 – 7.54: 6.85, 6.90, 7.00, 7.10, 7.35, 7.45 → Count: 6
3. 7.55 – 8.54: 7.55, 7.70, 7.98, 8.21, 8.35 → Count: 5
4. 8.55 – 9.54: 8.95, 9.25, 9.35 → Count: 3
5. 9.55 – 10.54: 10.10 → Count: 1

*(Check: 3 + 6 + 5 + 3 + 1 = 18. Correct.)*

Frequency Table:
| Time (seconds) | Frequency |
| :--- | :--- |
| 5.55 – 6.54 | 3 |
| 6.55 – 7.54 | 6 |
| 7.55 – 8.54 | 5 |
| 8.55 – 9.54 | 3 |
| 9.55 – 10.54 | 1 |

Step 2: Create a Histogram
* Draw bars for each time range.
* Heights should be: 3, 6, 5, 3, 1.

Step 3: Answer the Questions
* How many of the track-team members can run a mile in less than 7 minutes?
Look at the groups that are below 7.00.
The group 5.55 – 6.54 contains times like 5.96, 6.12, 6.52. All of these are less than 7.
The next group starts at 6.55 but goes up to 7.54. We need to check individual numbers in that group that are under 7.00.
From the sorted list for 6.55–7.54: 6.85, 6.90, 7.00, 7.10...
The times strictly *less than* 7 minutes are: 5.96, 6.12, 6.52, 6.85, 6.90.
Total count: 5 students.

* True or False: More than half of the team members take more than 8 minutes to run one mile.
Total team members = 18.
Half of the team = 9.
We need to count how many took *more* than 8 minutes.
Look at the groups starting above 8.00.
Group 8.55 – 9.54: 3 people.
Group 9.55 – 10.54: 1 person.
Group 7.55 – 8.54: This group includes numbers from 7.55 to 8.54. Which ones are greater than 8?
The numbers in this group are: 7.55, 7.70, 7.98, 8.21, 8.35.
The numbers greater than 8 are: 8.21, 8.35. (2 people).

Total people taking more than 8 minutes = 3 (from 8.55 group) + 1 (from 9.55 group) + 2 (from 7.55 group) = 6 people.

Is 6 more than half (9)? No.
Therefore, the statement is False.

Final Answer:
Part 1: Birth Years
* Frequency Table: 1990s: 10, 2000s: 10, 2010s: 10, 2020s: 10.
* Most-often decade: They all occur equally often (10 times each).
* True/False: False.

Part 2: Track Team
* Frequency Table:
* 5.55 – 6.54: 3
* 6.55 – 7.54: 6
* 7.55 – 8.54: 5
* 8.55 – 9.54: 3
* 9.55 – 10.54: 1
* Members running less than 7 minutes: 5
* True/False: False