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Given a table with student weights and heights, calculate and verify the 'Height in meter squared (m²)' and 'Body Mass Index (BMI)' columns.

Mathematics

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Step-by-step solution

4 steps
  1. Verify the "Height in meter squared (m²)" column for all students.

    For each student, the "Height in meter squared (m²)" value is calculated by squaring their "Height (m)". All values in this column are correctly calculated and rounded to two decimal places from the "Height (m)" column. For example:

    • Student 1: (1.75 m)2=3.0625 m2≈3.06 m2(1.75 \text{ m})^2 = 3.0625 \text{ m}^2 \approx 3.06 \text{ m}^2
    • Student 3: (1.58 m)2=2.4964 m2≈2.50 m2(1.58 \text{ m})^2 = 2.4964 \text{ m}^2 \approx 2.50 \text{ m}^2. The table shows 2.49 m22.49 \text{ m}^2, which is a minor rounding difference. We will use the table's value for BMI calculation.
    • Student 7: (1.56 m)2=2.4336 m2≈2.43 m2(1.56 \text{ m})^2 = 2.4336 \text{ m}^2 \approx 2.43 \text{ m}^2
  2. Calculate and verify the "Body Mass Index (BMI)" column for all students.

    We calculate BMI using the formula BMI=Weight (kg)Height (m)2\text{BMI} = \frac{\text{Weight (kg)}}{\text{Height (m)}^2}, using the "Height in meter squared (m²)" value from the table and rounding to one decimal place.

    • Student 1: 75 kg3.06 m2=24.509...≈24.5\frac{75 \text{ kg}}{3.06 \text{ m}^2} = 24.509... \approx 24.5. (Matches table)
    • Student 2: 64 kg2.37 m2=27.004...≈27.0\frac{64 \text{ kg}}{2.37 \text{ m}^2} = 27.004... \approx 27.0. (Matches table)
    • Student 3: 59 kg2.49 m2=23.694...≈23.7\frac{59 \text{ kg}}{2.49 \text{ m}^2} = 23.694... \approx 23.7. (Table shows 23.6, acceptable rounding)
    • Student 4: 68 kg2.62 m2=25.954...≈26.0\frac{68 \text{ kg}}{2.62 \text{ m}^2} = 25.954... \approx 26.0. (Table shows 25.9, acceptable rounding)
    • Student 5: 58 kg2.37 m2=24.472...≈24.5\frac{58 \text{ kg}}{2.37 \text{ m}^2} = 24.472... \approx 24.5. (Table shows 22.3, which is incorrect. The correct BMI is 24.5)
    • Student 6: 53 kg2.62 m2=20.229...≈20.2\frac{53 \text{ kg}}{2.62 \text{ m}^2} = 20.229... \approx 20.2. (Table shows 25.5, which is incorrect. The correct BMI is 20.2)
    • Student 7: 62 kg2.43 m2=25.514...≈25.5\frac{62 \text{ kg}}{2.43 \text{ m}^2} = 25.514... \approx 25.5. (Matches table)
    • Student 8: 62 kg2.62 m2=23.664...≈23.7\frac{62 \text{ kg}}{2.62 \text{ m}^2} = 23.664... \approx 23.7. (Table shows 23.6, acceptable rounding)
    • Student 9: 49 kg2.40 m2=20.416...≈20.4\frac{49 \text{ kg}}{2.40 \text{ m}^2} = 20.416... \approx 20.4. (Matches table)
    • Student 10: 56 kg2.19 m2=25.570...≈25.6\frac{56 \text{ kg}}{2.19 \text{ m}^2} = 25.570... \approx 25.6. (Table shows 25.5, acceptable rounding)
  3. List the corrected BMI values for all students.

    • Student 1: 24.5
    • Student 2: 27.0
    • Student 3: 23.7
    • Student 4: 26.0
    • Student 5: 24.5
    • Student 6: 20.2
    • Student 7: 25.5
    • Student 8: 23.7
    • Student 9: 20.4
    • Student 10: 25.6
  4. Determine the percentage of students who are obese.

    A person is considered obese if their Body Mass Index (BMI) is 30.0 or higher.
    Comparing the corrected BMI values to this criterion:

    • All students have a BMI less than 30.0. Number of obese students = 0 Total number of students = 10
    Percentage of obese students=010×100%=0%\text{Percentage of obese students} = \frac{0}{10} \times 100\% = \boxed{\text{0\%}}
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