find the first quartile of 7,8,7,9,11,8,7,9,6 and 8.

Step 1: Analyze the question We need the first quartile (Q1), the value below which 25% of the ordered data lies.

Step 2: Arrange the data in order The data: 7, 8, 7, 9, 11, 8, 7, 9, 6, 8 (n = 10)

Ordered: 6, 7, 7, 7, 8, 8, 8, 9, 9, 11

Step 3: Find Q1 Using the common method, Q1 is the median of the lower half.

Since n = 10, the lower half is the first 5 values: 6, 7, 7, 7, 8 The median of these is the 3rd value = 7.

Check with the position formula: Q1 position = ¼(n + 1) = ¼(11) = 2.75th value.

• 2nd value = 7, 3rd value = 7
• Q1 = 7 + 0.75(7 − 7) = 7

Both methods give 7.0.

Step 4: Verify with the cumulative frequency approach (often used in WASSCE) | x | 6 | 7 | 8 | 9 | 11 | |---|---|---|---|---|---| | f | 1 | 3 | 3 | 2 | 1 | | cf | 1 | 4 | 7 | 9 | 10 |

Q1 is at the ¼(10) = 2.5th position, which falls in the group with cf reaching 4, so x = 7. This agrees.

Answer: B (7.0).

Tip: Always sort the data first. For Q1, take the median of the lower half. If the 2nd and 3rd values (or the relevant neighbours) are equal, there's no need to interpolate. Also count carefully: here the data has 10 values, and it is easy to miss one.