Completing Two-Way Tables Worksheet | PDF Printable Measurement ... - Free Printable

Here are the solutions to the problems on the worksheet, broken down step-by-step.

Section A: Complete the two-way tables

Table 1: Cupcakes
* Chocolate Large: The total for Chocolate is missing, but we know the Small Total is 21 and Chocolate Small is 13. So, Strawberry Small = $21 - 13 = 8$.
* Now look at the Strawberry row. We have Small (8) and Large (18). Total Strawberry = $8 + 18 = 26$.
* Look at the Grand Total column. The total cupcakes sold is 60. We know Strawberry Total is 26. So, Chocolate Total = $60 - 26 = 34$.
* Finally, Chocolate Large = Chocolate Total (34) - Chocolate Small (13) = 21.
* Check Large Total: $21 (\text{Choc}) + 18 (\text{Straw}) = \mathbf{39}$.

| | Small | Large | Total |
| :--- | :---: | :---: | :---: |
| Chocolate | 13 | 21 | 34 |
| Strawberry | 8 | 18 | 26 |
| Total | 21 | 39 | 60 |

Table 2: School Students
* Right-handed Boy: Total Right-handed is 34. Right-handed Girl is 21. So, Boy = $34 - 21 = \mathbf{13}$.
* Left-handed Girl: Total students is 80. Total Right-handed is 34. So, Total Left-handed = $80 - 34 = \mathbf{46}$.
* We know Left-handed Boy is 16. So, Left-handed Girl = $46 - 16 = \mathbf{30}$.
* Totals:
* Total Boys = $13 (\text{Right}) + 16 (\text{Left}) = \mathbf{29}$.
* Total Girls = $21 (\text{Right}) + 30 (\text{Left}) = \mathbf{51}$.
* Check: $29 + 51 = 80$. Correct.

| | Boy | Girl | Total |
| :--- | :---: | :---: | :---: |
| Right-handed | 13 | 21 | 34 |
| Left-handed | 16 | 30 | 46 |
| Total | 29 | 51 | 80 |

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Section B

1) Homework Survey

a. Complete the two-way table
* Grade 7 Total: Given as 21.
* Grade 7 Less than an hour: Given as 16.
* Grade 7 More than an hour: Total (21) - Less (16) = 5.
* Grade 11 Total: Total students (50) - Grade 7 (21) = 29.
* Grade 11 More than an hour: Given as 22.
* Grade 11 Less than an hour: Total (29) - More (22) = 7.
* Column Totals:
* Less than an hour Total: $16 + 7 = \mathbf{23}$.
* More than an hour Total: $5 + 22 = \mathbf{27}$.

| | Grade 7 | Grade 11 | Total |
| :--- | :---: | :---: | :---: |
| Less than an hour | 16 | 7 | 23 |
| More than an hour | 5 | 22 | 27 |
| Total | 21 | 29 | 50 |

b. Use percentages to compare
* Grade 7: 16 out of 21 students do less than an hour.
* Percentage: $(16 \div 21) \times 100 \approx \mathbf{76\%}$.
* Grade 11: 7 out of 29 students do less than an hour.
* Percentage: $(7 \div 29) \times 100 \approx \mathbf{24\%}$.
* Comparison: A much higher percentage of Grade 7 students (76%) do less than an hour of homework compared to Grade 11 students (24%). Conversely, most Grade 11 students do more than an hour.

***

2) Commuters

a. Complete the two-way table
Since the problem gives percentages, we can assume a total of 100 commuters to make the math easy. The cells will represent percentages.

* Under 18 / Peak-time: Given as 4%.
* Off-peak Total: Given as 71%.
* Peak-time Total: Since Off-peak is 71%, Peak-time must be $100\% - 71\% = \mathbf{29\%}$.
* Over 18 Total: Given as 37%.
* Under 18 Total: Since Over 18 is 37%, Under 18 must be $100\% - 37\% = \mathbf{63\%}$.
* Under 18 / Off-peak: Total Under 18 (63%) - Under 18 Peak (4%) = 59%.
* Over 18 / Peak-time: Total Peak (29%) - Under 18 Peak (4%) = 25%.
* Over 18 / Off-peak: Total Over 18 (37%) - Over 18 Peak (25%) = 12%.
* *Check:* Does $59\% + 12\% = 71\%$ (Off-peak total)? Yes.

| | Under 18 | Over 18 | Total |
| :--- | :---: | :---: | :---: |
| Peak-time | 4% | 25% | 29% |
| Off-peak | 59% | 12% | 71% |
| Total | 63% | 37% | 100% |

b. Calculate percentage of commuters under 18 and travel during off-peak
Looking at the table we just completed, find the cell where "Under 18" and "Off-peak" meet.
The value is 59%.

Final Answer:
Section A
Cupcake Table Missing Values:
* Chocolate Large: 21
* Chocolate Total: 34
* Strawberry Small: 8
* Strawberry Total: 26
* Large Total: 39

Student Table Missing Values:
* Right-handed Boy: 13
* Left-handed Girl: 30
* Left-handed Total: 46
* Boy Total: 29
* Girl Total: 51

Section B
1a. Homework Table:
* Grade 7 / More than an hour: 5
* Grade 11 / Less than an hour: 7
* Grade 11 Total: 29
* Less than an hour Total: 23
* More than an hour Total: 27

1b. Comparison:
Approximately 76% of Grade 7 students do less than an hour of homework, while only about 24% of Grade 11 students do less than an hour. Grade 11 students do significantly more homework.

2a. Commuter Table (Percentages):
* Row 1 (Peak): Under 18: 4%, Over 18: 25%, Total: 29%
* Row 2 (Off-peak): Under 18: 59%, Over 18: 12%, Total: 71%
* Col Totals: Under 18: 63%, Over 18: 37%

2b. Percentage Calculation:
59%