The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.

Analyze the question: We need the third quartile (Q3) of 20 ordered scores.

Concept: Q3 is the value below which 75% of the data lies. Common methods:

• Position method: Q3 = ¾(n+1)th term
• Median-of-upper-half method: Q3 = median of the upper 10 scores

Ordered data (n = 20), numbered:

1. 44, 2. 47, 3. 48, 4. 49, 5. 50, 6. 51, 7. 52, 8. 53, 9. 53, 10. 54, 11. 58, 12. 59, 13. 60, 14. 61, 15. 63, 16. 65, 17. 67, 18. 70, 19. 73, 20. 75

Method 1 (upper half median): The upper half is the 11th to 20th terms: 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Its median is the average of the 5th and 6th of these: (63 + 65)/2 = 64.

Method 2 (¾(n+1)): ¾ × 21 = 15.75th term. The 15th term is 63 and the 16th is 65. Q3 = 63 + 0.75(65 − 63) = 63 + 1.5 = 64.5

This is not an option, so the intended method is the upper-half median, which gives exactly 64.

Answer: Q3 = 64, which is option C.

Tip: For WASSCE, when n is even, split the data into two equal halves. Q1 is the median of the lower half and Q3 is the median of the upper half. If your answer isn't among the options, check that you've used this method.