1. **Stating the problem:** We have 49 persons classified by weight intervals and their frequencies. We need to find: (i) The position of the median person in the ordered list by weight. (ii) The weight of the 22nd person. (iii) The median weight. 2. **Given data:** Weight intervals (kg): 30-40, 40-50, 50-60, 60-70, 70-80, 80-90 Number of persons: 8, 10, 10, 5, 4, 12 (sum = 49) 3. **Step (i): Find the median position.** The median position in an ordered list of $n$ persons is given by: $$\text{Median position} = \frac{n+1}{2}$$ Here, $n=49$, so: $$\frac{49+1}{2} = \frac{50}{2} = 25$$ So, the median is the weight of the person at the 25th position. 4. **Step (ii): Find the weight of the 22nd person.** Calculate cumulative frequencies: - Up to 30-40: 8 persons - Up to 40-50: 8 + 10 = 18 persons - Up to 50-60: 18 + 10 = 28 persons The 22nd person lies in the 50-60 kg interval because 18 < 22 ≤ 28. 5. **Step (iii): Calculate the median weight.** Median class is 50-60 kg. - Lower boundary $L = 50$ - Frequency of median class $f = 10$ - Cumulative frequency before median class $F = 18$ - Class width $h = 60 - 50 = 10$ Median formula: $$\text{Median} = L + \left(\frac{\frac{n+1}{2} - F}{f}\right) \times h$$ Substitute values: $$= 50 + \left(\frac{25 - 18}{10}\right) \times 10 = 50 + \left(\frac{7}{10}\right) \times 10 = 50 + 7 = 57$$ **Final answers:** (i) Median position = 25th person (ii) Weight of 22nd person lies in 50-60 kg interval (iii) Median weight = 57 kg