1. 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 |

2. 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 |

3. 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 |

4. 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 |

5. **English Translation:** Draw the **less than ogive** (cumulative frequency curve) for the following frequency distribution: | Marks Obtained | 50–60 | 60–70 | 70–80 | 80–90 | 90–100 | |----------------|-------|-------|-------|-------|--------| | Frequency | 4 | 8 | 12 | 6 | 10 |

6. Cumulative Frequency Table | Class Interval | Cumulative Frequency | |----------------------|----------------------| | Less than 10 | 6 | | Less than 20 | 10 | | Less than 30 | 18 | | Less than 40 | 30 | | Less than 50 | 46 |

7. 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.

8. > In a medical entrance examination, the frequency distribution of the marks obtained by 200 candidates is given below: > > | Marks Obtained | 400–450 | 450–500 | 500–550 | 550–600 | 600–650 | 650–700 | 700–750 | 750–800 | > |----------------|---------|---------|---------|---------|---------|---------|---------|---------| > | No. of Students| 20 | 30 | 28 | 26 | 24 | 22 | 18 | 32 | > > Draw an ogive curve and determine the median using it.

9. 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 |

10. 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 |

11. 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 |

12. 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 |

13. Using the direct method, calculate the mean of the following data: | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | |----------------|------|-------|-------|-------|-------| | Frequency | 4 | 6 | 10 | 6 | 4 |

14. 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 |

15. 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 | ---

16. 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 |

17. 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 |

18. Given below is a frequency distribution table: | Class Interval | 0–5 | 5–10 | 10–15 | 15–20 | 20–25 | 25–30 | |----------------|-----|------|-------|-------|-------|-------| | Frequency | 4 | 10 | 15 | 8 | 3 | 5 | Prepare a cumulative frequency table (greater than type) and draw a greater than ogive on graph paper.

19. 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 |

20. 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 |

21. 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 |

22. 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 |

23. 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 |

24. Determine the mode from the following frequency distribution table: | Class Interval | 0–50 | 50–100 | 100–150 | 150–200 | 200–250 | 250–300 | |----------------|------|--------|---------|---------|---------|---------| | Frequency | 10 | 16 | 28 | 22 | 18 | 6 |

25. Find the median from the following data: | Class Interval | 5–10 | 10–15 | 15–20 | 20–25 | 25–30 | 30–35 | 35–40 | 40–45 | |----------------|------|-------|-------|-------|-------|-------|-------|-------| | Frequency | 5 | 6 | 15 | 10 | 5 | 4 | 3 | 2 |

26. From the following frequency distribution of candidates' ages in an entrance examination, find the median: | Class Interval | 1–5 | 6–10 | 11–15 | 16–20 | 21–25 | 26–30 | 31–35 | |----------------|-----|------|-------|-------|-------|-------|-------| | Frequency | 2 | 3 | 6 | 7 | 5 | 4 | 3 |

27. From the following table, calculate the average marks of 52 students in Class 10 of a school using both the **direct method** and the **assumed mean method**: | Number of Students | 4 | 7 | 10 | 15 | 8 | 5 | 3 | |--------------------|---|---|----|----|---|---|---| | Marks |30 |33 | 35 | 40 |43 |45 |48 |

28. 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 |

29. **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 |

30. 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 |