Statistics — Important Questions

20

Step 1: Identify total students = 100, Cricket = 35, Football = 25, Basketball = 20. Step 2: Find students who chose Cricket, Football, and Basketball: 35 + 25 + 20 = 80 students. Step 3: Calculate remaining students for Tennis: Total - (Cricket + Football + Basketball) = 100 - 80. Step 4: Final calculation: 100 - 80 = 20 students chose Tennis. Verify: 35 + 25 + 20 + 20 = 100 ✓.

4

Step 1: In histograms with equal class widths, the height of rectangles is proportional to frequency. Step 2: Frequency of first interval (10-15) = 8, Frequency of second interval (15-20) = 12. Step 3: Since widths are equal, height difference = frequency difference = 12 - 8. Step 4: Calculate: 12 - 8 = 4. The difference in heights of the rectangles is 4 units.

5

Step 1: Class size is calculated as Upper limit - Lower limit for any interval. Step 2: Take the first interval 0-5: Upper limit = 5, Lower limit = 0. Step 3: Calculate class size: 5 - 0 = 5. Step 4: Verify with another interval 5-10: 10 - 5 = 5. All intervals have the same class size of 5.

20-30

Step 1: The mode class is the class with the highest frequency. Find the highest frequency from y-coordinates: 2, 6, 10, 8, 4. Step 2: The maximum frequency is 10, corresponding to x-coordinate 25. Step 3: Since 25 is the class mark and class width is 10, find the interval: Class mark = (Lower + Upper)/2, so 25 = (Lower + Upper)/2. Step 4: For width 10: Lower = 25 - 5 = 20, Upper = 25 + 5 = 30. The mode class interval is 20-30.