1. Got it! Here's the cleaned-up version without the bold formatting: Determine the mode from the following frequency distribution: | Item Size Number | 4–8 | 8–12 | 12–16 | 16–20 | 20–24 | 24–28 | 28–32 | |------------------|-----|------|-------|-------|-------|-------|-------| | Frequency | 9 | 10 | 18 | 14 | 10 | 6 | 3 |

2. Find the median from the following grouped frequency distribution: | Class Interval | Frequency | |----------------|-----------| | 0–10 | 4 | | 10–20 | 7 | | 20–30 | 10 | | 30–40 | 15 | | 40–50 | 10 | | 50–60 | 8 | | 60–70 | 5 |

3. From the following cumulative frequency distribution table, construct a frequency distribution table and determine the **mode** of the data: | Class Boundary | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 | Less than 60 | Less than 70 | Less than 80 | |--------------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------| | Cumulative Frequency | 4 | 16 | 40 | 76 | 96 | 112 | 120 | 125 |

4. Calculate the average marks obtained by the students, given the following cumulative frequency distribution: | Marks | Number of Students | |--------------|--------------------| | Less than 10 | 6 | | Less than 20 | 10 | | Less than 30 | 18 | | Less than 40 | 30 | | Less than 50 | 46 |

5. Draw a greater cumulative frequency ogive using the following statistical distribution and determine the median from it: | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | |---------------------|------|--------|--------|--------|--------|--------| | Frequency | 8 | 12 | 21 | 30 | 22 | 7 |

6. Calculate the average (mean) from the following frequency distribution table: | Class Interval | 45–54 | 55–64 | 65–74 | 75–84 | 85–94 | 95–104 | |----------------|-------|-------|-------|-------|-------|--------| | Frequency | 8 | 13 | 19 | 32 | 12 | 6 |

7. Given that the combined (weighted) mean of the following frequency distribution is 50 and the total frequency is 120, find the values of \( f_1 \) and \( f_2 \). | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|--------|--------|--------|---------| | Frequency | 17 | \( f_1 \) | 32 | \( f_2 \) | 19 |

8. Find the mode from the following grouped frequency distribution: | Class Interval | Frequency | |----------------|-----------| | 3–6 | 2 | | 6–9 | 6 | | 9–12 | 12 | | 12–15 | 24 | | 15–18 | 21 | | 18–21 | 12 | | 21–24 | 3 |

9. Given that the combined mean of the following distribution is 50 and the total frequency is 120, find the values of \(f_1\) and \(f_2\): | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|--------|--------|--------|---------| | Frequency | 17 | \(f_1\) | 32 | \(f_2\) | 19 |

10. Prepare a greater-than cumulative frequency table from the following frequency distribution and draw an ogive on graph paper. | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | |----------------|------|--------|--------|--------|--------|--------| | Frequency | 7 | 10 | 23 | 50 | 6 | 4 |

11. Find the mode of the following frequency distribution: | Class Interval | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 | 100–109 | |----------------|--------|--------|--------|--------|--------|----------| | Frequency | 5 | 20 | 40 | 50 | 30 | 6 |

12. Find the median of the following frequency distribution: | Class Interval | 0–10 | 10–30 | 30–60 | 60–70 | 70–90 | |----------------|------|-------|-------|-------|-------| | Frequency | 15 | 25 | 30 | 4 | 10 |

13. If the mean of the frequency distribution is 62.8 and the total frequency is 50, then what are the values of \(x\) and \(y\) given the following table: | Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | 100–120 | |-------------|------|--------|--------|--------|---------|----------| | Frequency | 5 | \(x+y\) | 10 | \(y−x\) | 7 | 8 |

14. Find the median from the following frequency distribution: | Number Range (\(x_i\)) | 0–4 | 5–9 | 10–14 | 15–19 | 20–24 | 25–29 | 30–34 | 35–39 | |------------------------|-----|-----|-------|-------|-------|-------|-------|-------| | Frequency (\(f_i\)) | 4 | 5 | 7 | 8 | 7 | 5 | 6 | 3 |

15. Create a cumulative frequency (less than type) table from the given data and draw an ogive on graph paper. | Class Interval | 0–10 | 10–20 | 20–30 | |----------------|------|-------|-------| | Frequency | 1 | 6 | 15 | | Class Interval | 30–40 | 40–50 | 50–60 | 60–70 | |----------------|--------|--------|--------|--------| | Frequency | 20 | 15 | 6 | 1 |

16. Find the median of the following frequency distribution: | Class Interval | 1–5 | 6–10 | 11–15 | 16–20 | 21–25 | 26–30 | 31–35 | |----------------|-----|------|--------|--------|--------|--------|--------| | Frequency | 2 | 3 | 6 | 7 | 5 | 4 | 3 |

17. To draw the less than ogive (ক্ষুদ্রতর সূচক ওজাইভ), first calculate the cumulative frequency: | Class Interval | Frequency | Cumulative Frequency (Less Than) | |----------------|-----------|----------------------------------| | Less than 5 | 4 | 4 | | Less than 10 | 10 | 14 | | Less than 15 | 15 | 29 | | Less than 20 | 8 | 37 | | Less than 25 | 3 | 40 | | Less than 30 | 5 | 45 | Plot the cumulative frequency against the upper class boundaries: 5, 10, 15, 20, 25, 30. Connect the points smoothly to form the ogive.

18. If the median of the following data is 32 and the total frequency is 100, find the values of \(x\) and \(y\): | Class Interval | 0–10 | 10–20 | 20–30 | |----------------|------|--------|--------| | Frequency | 10 | \(x\) | 25 | | Class Interval | 30–40 | 40–50 | 50–60 | |----------------|--------|--------|--------| | Frequency | 30 | \(y\) | 10 |

19. Find the mode of the following frequency distribution: | Class Interval | 0–5 | 5–10 | 10–15 | |----------------|-----|------|--------| | Frequency | 5 | 12 | 18 | | Class Interval | 15–20 | 20–25 | 25–30 | 30–35 | |----------------|--------|--------|--------|--------| | Frequency | 28 | 17 | 12 | 8 |

20. If the combined (weighted) mean of the following frequency distribution table is 54, then find the value of K: | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|-------|-------|-------|--------| | Frequency | 7 | 11 | K | 9 | 13 |

21. Let's calculate the average from the following data: | Class Interval | 5–14 | 15–24 | 25–34 | 35–44 | 45–54 | 55–64 | |----------------|------|-------|-------|-------|-------|-------| | Frequency | 3 | 6 | 18 | 20 | 10 | 3 |

22. Let's find the mode from the following frequency distribution: | Class Interval | 0–5 | 5–10 | 10–15 | 15–20 | 20–25 | 25–30 | 30–35 | |----------------|-----|------|-------|-------|-------|-------|-------| | Frequency | 5 | 12 | 18 | 28 | 17 | 12 | 8 |

23. Based on the given data, prepare a cumulative frequency (greater than type) table and draw an ogive on graph paper: | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | |----------------|------|-------|-------|-------|-------|-------| | Frequency | 7 | 10 | 23 | 50 | 6 | 4 |

24. **Find the average (mean) of the following data:** | Class Interval | 5–14 | 15–24 | 25–34 | 35–44 | 45–54 | 55–64 | |----------------|------|-------|-------|-------|-------|-------| | Frequency | 3 | 6 | 18 | 20 | 10 | 3 |

25. Determine the mode of the following frequency distribution: | Class Interval | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | |---------------|------|------|------|------|------|------|------| | Frequency | 5 | 12 | 18 | 28 | 17 | 12 | 8 |

26. Let's determine the mode from the frequency distribution below: | Class Interval | 45–54 | 55–64 | 65–74 | 75–84 | 85–94 | 95–104 | |--------------------|--------|--------|--------|--------|--------|---------| | Frequency | 4 | 6 | 40 | 76 | 96 | 112 |

27. The ages of 100 people present at a program are given in the table below. Calculate the average age of these 100 people using any appropriate method. | Age (in years) | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | |----------------|-------|-------|-------|-------|-------|-------| | Number of people | 08 | 12 | 20 | 22 | 18 | 20 |

28. If the median of the following data is 32 and \(x + y = 100\), determine the values of \(x\) and \(y\). | Class Interval | 0–10 | 10–20 | 20–30 | |----------------|------|-------|-------| | Frequency | 10 | x | 25 | | Class Interval | 30–40 | 40–50 | 50–60 | |----------------|--------|--------|--------| | Frequency | 30 | y | 10 | ---

29. If the median of the following frequency distribution table is 27, then find the value of \(a\): | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | |----------------|------|--------|--------|--------|--------| | Frequency | 3 | a | 20 | 12 | 7 |

30. Calculate the mean using the assumed mean method (step-deviation method) from the following data: | Class Interval | 0–30 | 30–60 | 60–90 | 90–120 | 120–150 | |----------------|------|--------|--------|---------|----------| | Frequency | 12 | 15 | 20 | 25 | 8 |