NECO 2005 Mathematics · Question 30

3 - 7, 8 - 12, 13 - 17, 18 - 22. Which of the following is/are true? I. The class Interval is 4 II. The class…

Question

3 - 7, 8 - 12, 13 - 17, 18 - 22. Which of the following is/are true? I. The class Interval is 4 II. The class boundaries are 2.5, 7.5, 12.5, 18.5, 22.5 III. The mid-marks are 5, 10, 15, and 20

A.I only
B.II only
C.III only
D.I and II only
E.I and III only

Answer: C. III only

Explanation written with AI and checked against the answer key

Analyze the question: The classes are 3-7, 8-12, 13-17, 18-22. We check each statement.

Concepts:

Class boundaries lie halfway between the upper limit of one class and the lower limit of the next.
Class size (interval) = upper boundary − lower boundary.
Mid-mark = (lower limit + upper limit) ÷ 2.

Statement I: The class interval is 4. For 3-7, the boundaries are 2.5 and 7.5, so the class size = 7.5 − 2.5 = 5. Also, the lower limits 3, 8, 13, 18 differ by 5. The class interval is 5, not 4 (4 is only the difference 7 − 3). I is false.

Statement II: The class boundaries are 2.5, 7.5, 12.5, 18.5, 22.5. The correct boundaries are 2.5, 7.5, 12.5, 17.5, 22.5. The list has 18.5 instead of 17.5. II is false.

Statement III: The mid-marks are 5, 10, 15, 20.

3-7: (3+7)/2 = 5
8-12: (8+12)/2 = 10
13-17: (13+17)/2 = 15
18-22: (18+22)/2 = 20

III is true.

Answer: Only III is true, so the correct option is C.

Tip: Watch for small traps like 18.5 instead of 17.5 in boundary lists. Also remember that class size is the difference between boundaries (or between consecutive lower limits), not the difference between the limits within one class.

AI can make mistakes. Report anything that looks wrong.