10. Cumulative frequency (less-than) of marks of 800 students:
| Marks | Below 10 | Below 20 | Below 30 | Below 40 | Below 50 | Below 60 | Below 70 | Below 80 | Below 90 | Below 100 |
|---|---|---|---|---|---|---|---|---|---|---|
| No. of students | 10 | 50 | 130 | 270 | 440 | 570 | 670 | 740 | 780 | 800 |
Construct the (ordinary) frequency distribution table.
| Class | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 | 80–90 | 90–100 |
|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 10 | 40 | 80 | 140 | 170 | 130 | 100 | 70 | 40 | 20 |
Step 1: Read the given data carefully. The table shows cumulative frequencies (less–than type). For example, “Below 30 = 130” means that 130 students scored less than 30 marks.
Step 2: To convert cumulative frequencies into ordinary frequencies, we need to subtract consecutive values. Why? Because cumulative means “total so far”. Ordinary frequency means “number of students in that specific interval”.
Step 3: Start with the first class (0–10). - Below 10 = 10. - This is the first cumulative value, so frequency for 0–10 = 10.
Step 4: Now calculate the second class (10–20). - Below 20 = 50. - Below 10 = 10. - Frequency for 10–20 = 50 – 10 = 40.
Step 5: For the third class (20–30): - Below 30 = 130. - Below 20 = 50. - Frequency = 130 – 50 = 80.
Step 6: For the fourth class (30–40): - Below 40 = 270. - Below 30 = 130. - Frequency = 270 – 130 = 140.
Step 7: For the fifth class (40–50): - Below 50 = 440. - Below 40 = 270. - Frequency = 440 – 270 = 170.
Step 8: For the sixth class (50–60): - Below 60 = 570. - Below 50 = 440. - Frequency = 570 – 440 = 130.
Step 9: For the seventh class (60–70): - Below 70 = 670. - Below 60 = 570. - Frequency = 670 – 570 = 100.
Step 10: For the eighth class (70–80): - Below 80 = 740. - Below 70 = 670. - Frequency = 740 – 670 = 70.
Step 11: For the ninth class (80–90): - Below 90 = 780. - Below 80 = 740. - Frequency = 780 – 740 = 40.
Step 12: For the tenth class (90–100): - Below 100 = 800. - Below 90 = 780. - Frequency = 800 – 780 = 20.
Step 13: Now write the ordinary frequency distribution table:
| Class | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 | 80–90 | 90–100 |
|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 10 | 40 | 80 | 140 | 170 | 130 | 100 | 70 | 40 | 20 |
Final Check: Add all frequencies: 10 + 40 + 80 + 140 + 170 + 130 + 100 + 70 + 40 + 20 = 800. This matches the total number of students given. ✔️