Final Answer:
1. a. Completed table (right side):
- Grade 7: Can swim = 120, Cannot swim = 60, Total = 180
- Grade 8: Can swim = 168, Cannot swim = 11, Total = 179
- Grade 9: Can swim = 172, Cannot swim = 3, Total = 175
- Total: Can swim = 460, Cannot swim = 74, Total = 534
b. 74 students need swimming lessons.
c. 179 students in grade 8.
d. 60 seventh-grade students cannot swim.
e. 120 + 168 = 288 students in grades 7 and 8 can swim.
f. 180 + 179 + 175 = 534 students altogether.
g. Two-way relative frequency table (divide each cell by 534):
- Grade 7: Can swim ≈ 0.225, Cannot swim ≈ 0.112
- Grade 8: Can swim ≈ 0.315, Cannot swim ≈ 0.021
- Grade 9: Can swim ≈ 0.322, Cannot swim ≈ 0.006
- Totals: Can swim ≈ 0.861, Cannot swim ≈ 0.139
h. Relative frequency of grade 8 & cannot swim = 11/534 ≈ 0.021
i. % of grade 9 who can swim = (172/175) × 100 ≈ 98.3%
j. % who cannot swim = (74/534) × 100 ≈ 13.9%
k. % who are grade 9 = (175/534) × 100 ≈ 32.8%
2. a. Completed table (bottom row):
- Boys total = 40 + 55 + 161 = 256
- Girls total = 36 + 55 + 144 = 235
- Always wears: 40 + 36 = 76
- Sometimes wears: 55 + 55 = 110
- Never wears: 161 + 144 = 305
- Grand total = 256 + 235 = 491 (but problem says 484 — likely typo; use given totals to adjust: if total is 484, then one value must be off — but per data, sums give 491. We’ll use the numbers as given and assume total = 491 for consistency.)
However, since problem states “a principal… collected information about 484 students”, we reconcile:
Given: Boys total = 40+55+161 = 256
Girls total = 36+55+144 = 235
256 + 235 = 491 ≠ 484 → discrepancy of 7. But since no correction is indicated, we proceed with raw data as given (likely typo in problem). For answers, use the table values directly.
b. 55 boys sometimes wear glasses.
c. 55 + 36 = 91 students wear glasses some of the time (boys + girls who sometimes wear).
d. 161 + 144 = 305 students never wear glasses.
e. Boys = 256, Girls = 235 → more boys.
f. Two-way relative frequency table (divide each cell by 491):
- Boys: Always ≈ 0.081, Sometimes ≈ 0.112, Never ≈ 0.328
- Girls: Always ≈ 0.073, Sometimes ≈ 0.112, Never ≈ 0.293
- Totals: Always ≈ 0.154, Sometimes ≈ 0.224, Never ≈ 0.621
g. Relative frequency of girls who never wear = 144/491 ≈ 0.293
h. % of girls who never wear = (144/235) × 100 ≈ 61.3%
i. % who are boys = (256/491) × 100 ≈ 52.1%
j. % who always wear = (76/491) × 100 ≈ 15.5%
Parent Tip: Review the logic above to help your child master the concept of two way frequency tables worksheet.
