Data Handling — Important Questions

5/6

Step 1: Factors of 6 from 1-6 are: 1, 2, 3, 6. Numbers greater than 4: 5, 6. Step 2: Union of these sets = {1, 2, 3, 5, 6} (6 appears in both sets but counted once). Step 3: Number of favourable outcomes = 5. Step 4: Total outcomes = 6. Probability = 5/6. Common mistake: Students often add both sets separately getting 4+2=6 and write 6/6=1, forgetting that 6 is counted twice (double-counting error).

77.6°

Step 1: Total marks = 45 + 60 + 55 + 70 + 45 = 275. Step 2: Fraction for the student who scored 60 = 60/275. Step 3: Central angle = (60/275) × 360° = 21600/275 = 78.54°. Hmm, let me recalculate: 60/275 × 360 = 60 × 360 / 275 = 21600/275 ≈ 78.5°. So 78.5° is actually closer. Step 4: The answer 78.5° is correct. Common mistake: Adding marks incorrectly or forgetting to multiply the fraction by 360°.

13/20

Step 1: Using the addition rule: n(Cricket OR Football) = n(Cricket) + n(Football) - n(Both). Step 2: = 18 + 15 - 7 = 26. Step 3: Probability = 26/40 = 13/20. Step 4: Verification: 26 students like at least one sport out of 40. 13/20 = 0.65. Common mistake: Adding 18 + 15 = 33 without subtracting the 7 students counted twice, giving wrong answer 33/40.

20%

Step 1: Central angle for clothing = 192° - 120° = 72°. Step 2: Percentage = (central angle / 360°) × 100. Step 3: = (72/360) × 100 = (1/5) × 100 = 20%. Step 4: So clothing accounts for 20% of total expenditure. Common mistake: Students sometimes use 120° or 192° directly instead of finding the difference between the two angles to get the sector's angle.