The table below shows the frequency distribution of the number of siblings reported by a group of 25 students. Number...

1. TRANSLATE the problem information

• Given information:
  • Frequency table showing number of siblings and how many students reported each number
  • Total of 25 students
  • Need to find the median (middle value)

2. INFER the approach

• The median is the middle value when all 25 data points are arranged in order
• For 25 data points (odd number), the median is at position \(\frac{25+1}{2} = 13\)
• We need to figure out which "number of siblings" value is at the 13th position

3. SIMPLIFY by finding cumulative positions

• Start from the lowest value and count up:
  • First 6 students (positions 1-6): reported 0 siblings
  • Next 9 students (positions 7-15): reported 1 sibling
  • Next 7 students (positions 16-22): reported 2 siblings
  • Last 3 students (positions 23-25): reported 3 siblings

4. INFER where the 13th position falls

• The 13th position needs to fall somewhere in the range from position 7 to position 15
• All students in positions 7-15 reported having 1 sibling
• Therefore, the student at the 13th position reported 1 sibling

Answer: A (1)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students confuse the frequency values with the actual data values. They might think that since 9 is the highest frequency, the median should be 9, leading them to select Choice D (9).

Second Most Common Error:

Poor INFER strategy: Students try to find the "average" of the number of siblings (0, 1, 2, 3) instead of finding the middle value of the actual 25 data points. This might lead them to calculate \(\frac{0+1+2+3}{4} = 1.5\), causing them to select Choice B (1.5).

The Bottom Line:

This problem requires students to understand that frequency tables represent multiple data points, not just the categories themselves. The key insight is converting frequencies into actual positions in an ordered list of all 25 students.