The intervals should be from 25-34,35-44 and so on

Thank you for the clarification. Let's adjust the intervals as specified:

### Adjusted Problem Breakdown:
1. **Data Given:** Annual profits (in thousands of rupees) categorized in intervals:
   - 25-34
   - 35-44
   - 45-54
   - 55-64
   - 65-74
   - 75-84
   - 85-94
   - 95-104

2. **Tasks:**
   - (i) Determine the number of firms having profits between ₹25,000 and ₹64,000.
   - (ii) Identify the profit class with the highest frequency.
   - (iii) Calculate the median profit group.

### Updated Steps to Solve:

1. **Constructing the Frequency Table:**
   The table will display profit intervals (class intervals) and corresponding frequencies (number of firms).

2. **Calculating Number of Firms with Profits between ₹25,000 and ₹64,000:**
   Sum the frequencies corresponding to the profit intervals 25-34, 35-44, 45-54, and 55-64.

3. **Finding the Class with Maximum Firms:**
   Identify the class interval with the highest frequency in the table.

4. **Calculating the Median Class:**
   The median class is the class interval in which the cumulative frequency reaches or exceeds half of the total number of firms.

### Let's Solve:

1. **Class Intervals and Frequencies (Based on Data in the Image):**

   | Profit (₹000) | Frequency |
   |---------------|-----------|
   | 25-34         | 4         |
   | 35-44         | 5         |
   | 45-54         | 13        |
   | 55-64         | 20        |
   | 65-74         | 14        |
   | 75-84         | 5         |
   | 85-94         | 3         |
   | 95-104        | 2         |

2. **Number of Firms with Profits between ₹25,000 and ₹64,000:**
   - \(4 + 5 + 13 + 20 = 42\) firms.

3. **Class with Maximum Firms:**
   - The class interval \(55-64\) has the highest frequency of 20 firms.

4. **Median Class:**
   - Cumulative Frequency:
     - 25-34: 4
     - 35-44: 9
     - 45-54: 22
     - 55-64: 42
     - 65-74: 56
     - 75-84: 61
     - 85-94: 64
     - 95-104: 66

   The cumulative frequency exceeds 33 (which is half of 66) at the class interval 55-64. Thus, the median class is **55-64**.

### Final Answers:
1. **Number of Firms with Profits between ₹25,000 and ₹64,000:** 42 firms.
2. **Profit Class with the Maximum Firms:** ₹55,000 - ₹64,000.
3. **Median Profit Class:** ₹55,000 - ₹64,000.

Would you like any further details or have any questions?

### Related Questions:
1. How do you calculate the mean of the given data?
2. What is the mode of this distribution, and how can you find it?
3. How would you compute the standard deviation of the profit data?
4. What are the steps to calculate the quartiles of the distribution?
5. How can the data be graphically represented for better analysis?

### Tip:
When working with frequency distributions, the median is a useful measure as it divides the data into two equal parts, providing insight into the distribution's central tendency.

Explore how to analyze profit intervals ranging from ₹25,000 to ₹104,000. Learn how to calculate the number of firms within specific profit ranges, identify the profit class with the highest frequency, and determine the median profit class. Suitable for advanced high school students or anyone interested in statistical analysis of business data.

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