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Mean and median · 3 problems
From the 15Q20M Grade 6 workbook (Days 76–79) · Pencil, no calculator
Name:
- 1.
A data set is 2, 4, 6, 12. What is the difference between its mean and its median?
Answer:
- 2.
Which data set has a median of 7 and a range of 6?
A4, 6, 10
B5, 7, 9
C4, 7, 12
D4, 7, 10
- 3.
Three quizzes have a mean of 8 points. After a fourth quiz of 12 points, what is the new mean?
Answer:
Answer key (for parents)
Answer key: Mean and median
- 1.
1
Mean: 2 + 4 + 6 + 12 = 24, and 24 ÷ 4 = 6. Median: the list is in order and has two middle numbers, 4 and 6, so the median is (4 + 6) ÷ 2 = 5. Difference: 6 − 5 = 1.
- 2.
D (4, 7, 10)
Check both conditions for each set. 4, 7, 10 has median 7 and range 10 − 4 = 6. 4, 6, 10 has median 6. 5, 7, 9 has range 4. 4, 7, 12 has range 8. Only 4, 7, 10 works.
- 3.
9
A mean of 8 over three quizzes means 8 × 3 = 24 points in all. Add the fourth quiz: 24 + 12 = 36. Divide by four quizzes: 36 ÷ 4 = 9.
Equivalent answers count as correct: 2/4 for 1/2, 0.5 for 1/2, and so on.
For parents
Answer key: Mean and median
- 1.
1
Mean: 2 + 4 + 6 + 12 = 24, and 24 ÷ 4 = 6. Median: the list is in order and has two middle numbers, 4 and 6, so the median is (4 + 6) ÷ 2 = 5. Difference: 6 − 5 = 1.
- 2.
D (4, 7, 10)
Check both conditions for each set. 4, 7, 10 has median 7 and range 10 − 4 = 6. 4, 6, 10 has median 6. 5, 7, 9 has range 4. 4, 7, 12 has range 8. Only 4, 7, 10 works.
- 3.
9
A mean of 8 over three quizzes means 8 × 3 = 24 points in all. Add the fourth quiz: 24 + 12 = 36. Divide by four quizzes: 36 ÷ 4 = 9.
Equivalent answers count as correct: 2/4 for 1/2, 0.5 for 1/2, and so on.