Construct the frequency distribution table from the following cumulative frequency table:
`{:("Ages" ,"No of Students"),("Below" 4,0),("Below" 7,85),("Below" 10,140),("Below" 13,243),("Below" 16,300):}`
State the number of students in the age group 10-13

Answer

To construct the frequency distribution table from the given cumulative frequency table, we will follow these steps:

### Step 1: Identify Class Intervals
From the cumulative frequency table, we can identify the class intervals based on the "Below" values:
- Below 4
- Below 7
- Below 10
- Below 13
- Below 16

### Step 2: Determine Frequency for Each Class Interval
We will calculate the frequency for each class interval by subtracting the cumulative frequency of the previous interval from the cumulative frequency of the current interval.

1. **For the interval 0 to 4:**
- Cumulative frequency below 4 = 0
- Frequency = 0 (as there are no students in this age group)

2. **For the interval 4 to 7:**
- Cumulative frequency below 7 = 85
- Cumulative frequency below 4 = 0
- Frequency = 85 - 0 = 85

3. **For the interval 7 to 10:**
- Cumulative frequency below 10 = 140
- Cumulative frequency below 7 = 85
- Frequency = 140 - 85 = 55

4. **For the interval 10 to 13:**
- Cumulative frequency below 13 = 243
- Cumulative frequency below 10 = 140
- Frequency = 243 - 140 = 103

5. **For the interval 13 to 16:**
- Cumulative frequency below 16 = 300
- Cumulative frequency below 13 = 243
- Frequency = 300 - 243 = 57

### Step 3: Construct the Frequency Distribution Table
Now we can compile the frequencies into a table format:

| Age Group | Frequency |
|-------------|-----------|
| 0 - 4 | 0 |
| 4 - 7 | 85 |
| 7 - 10 | 55 |
| 10 - 13 | 103 |
| 13 - 16 | 57 |

### Step 4: State the Number of Students in the Age Group 10-13
From the frequency distribution table, we can see that the number of students in the age group 10 to 13 is 103.

### Final Answer
The number of students in the age group 10-13 is **103**.

---