here is the histogram in text format: _weight (kg) | no. of boys | frequency_ 40-50 | 7 | 0.07 50-70 | 18 | 0.18 70-90 | 16 | 0.16 90-100 | 5 | 0.5

It seems you have provided data in the form of a histogram. Here's how we interpret this:

| Weight (kg) | No. of Boys | Frequency |
|-------------|--------------|-----------|
| 40-50       | 7            | 0.07      |
| 50-70       | 18           | 0.18      |
| 70-90       | 16           | 0.16      |
| 90-100      | 5            | 0.05      |

### Key Insights:
1. **Total Number of Boys:**
   The total number of boys can be calculated by summing up the "No. of Boys" column:
   \[
   \text{Total} = 7 + 18 + 16 + 5 = 46 \text{ boys}
   \]

2. **Verifying Frequency:**
   The frequency represents the proportion of boys in each weight range. Let's verify if the frequencies sum up to 1, as they should for a complete dataset:
   \[
   0.07 + 0.18 + 0.16 + 0.05 = 0.46
   \]
   This indicates an issue with the frequency values, as they do not sum up to 1. If this is based on relative frequency, it should ideally match the ratio between the count in each range and the total count. 

   Let's recompute the correct frequencies based on the total count of 46 boys:
   \[
   \text{Frequency for 40-50} = \frac{7}{46} \approx 0.152
   \]
   \[
   \text{Frequency for 50-70} = \frac{18}{46} \approx 0.391
   \]
   \[
   \text{Frequency for 70-90} = \frac{16}{46} \approx 0.348
   \]
   \[
   \text{Frequency for 90-100} = \frac{5}{46} \approx 0.109
   \]
   
   These frequencies sum up to approximately 1, indicating a correct distribution.

3. **Weight Range with the Most Boys:**
   The range **50-70 kg** has the highest number of boys, with 18 boys, representing approximately 39.1% of the total boys.

4. **Smallest Weight Range:**
   The range **90-100 kg** has the fewest boys, with only 5 boys, making up about 10.9% of the total.

5. **Interpretation of the Data:**
   Most boys fall within the middle ranges (50-90 kg), and very few boys are in the extreme ranges (below 50 kg or above 90 kg).

Would you like more details or have any questions about this?  

### Related Questions:
1. How do we calculate cumulative frequencies from the given data?
2. What is the percentage of boys weighing between 70-100 kg?
3. How can we represent this histogram visually?
4. How is the mean weight of the boys computed from this data?
5. How can we calculate the variance of the weights based on this table?

### Tip:
When verifying frequency tables, always check that the sum of the frequencies equals 1 (or 100%, depending on format). If not, adjust based on total counts.

Analyze a histogram with weight ranges from 40-100 kg and frequency distribution for a group of boys. Learn how to calculate the total number of boys, verify frequencies, and understand the distribution in a step-by-step solution. Suitable for Grades 6-8.

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