1. 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 |

2. From the following frequency distribution table of candidates' ages in an entrance examination, find the **mode**: | Age (in years) | 16–18 | 18–20 | 20–22 | 22–24 | 24–26 | |----------------|--------|--------|--------|--------|--------| | Number of Candidates | 45 | 75 | 38 | 22 | 20 |

3. 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 | ---

4. 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 |

5. 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 |

6. 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 |

7. 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 |

8. 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 |

9. > 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.

10. 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 |

11. 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 |

12. 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 |

13. Here is the English translation: Values related to A and B are: | | A | B | |-----|-----|-----| | | 25 | 10 | | | 30 | 12 | | | 45 | 18 | | | 250 | 100 | Determine if there is any proportional relationship between A and B, and find the constant of proportionality if it exists.

14. 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 |

15. 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 |

16. **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 |

17. 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 |

18. 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 |

19. 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 |

20. 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 |

21. 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 |

22. 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 |

23. 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 |

24. 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 |

25. 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 |