Which of the following conclusions is false?

Circle graph of number of books read by students over the summer with 5 sections, showing that 18% of students read only 1 book, 24% read 2 books, 42% read 3 books, 12% read 4 books, and 4% read 5 or more books

(1 point)
Responses

If 50 students read four books, then 100 students read two books.

If 50 students read four books, then 100 students read two books.

If the summer reading requirement was to read at least three books, then 42% of the students did not meet the requirement.

If the summer reading requirement was to read at least three books, then 42% of the students did not meet the requirement.

Only four students read five or more books.

Only four students read five or more books.

Sixteen percent of the students read four or more books.

Sixteen percent of the students read four or more books.

1 answer

To evaluate which conclusion is false, let's analyze each statement based on the percentages given from the circle graph:

  1. If 50 students read four books, then 100 students read two books.

    • 12% of students read four books.
    • If 50 students read four books, that represents 12% of the total students. Therefore, the total number of students can be calculated as: \[ \text{Total students} = \frac{50}{0.12} \approx 416.67 \text{ (not possible, so let's use whole numbers)} \]
    • If we take 50 as the base, you can calculate it using a reasonable whole number:
      • Let’s assume about 417 total, which gives an approximation of students.
      • In this case, total would be about 100 for those who read two books.
    • This statement seems plausible.
  2. If the summer reading requirement was to read at least three books, then 42% of the students did not meet the requirement.

    • 42% of students read 3 books, which means they met the requirement.
    • The remaining percentages (18% for 1 book + 24% for 2 books + 12% for 4 books + 4% for 5 or more books) add up to 58%, meaning those didn't meet it.
    • Therefore, this statement is false.
  3. Only four students read five or more books.

    • 4% of students read five or more books.
    • If we assume 417 students (as previously calculated), then 4% of this would indeed be around 16-17 students who read 5 or more books, not four.
    • This statement is false.
  4. Sixteen percent of the students read four or more books.

    • Students who read 4 books make up 12%, and those who read 5 or more comprise 4%.
    • Thus, the total percentage for reading 4 or more is 12% + 4% = 16%.
    • This statement is true.

Now, looking at the summaries:

  • The second statement about 42% not meeting the requirement is true based on our calculations.
  • The statement claiming "Only four students read five or more books" is indeed false when evaluated.

Therefore, the false conclusion is “Only four students read five or more books.”