Interpreting Graphs - Free Printable

The image shows a frequency distribution graph of worm lengths, with the following features:

- X-axis: Length of worms in centimeters (from 4.0 cm to 9.0 cm)
- Y-axis: Number of worms (frequency)
- A smooth curve represents the distribution of worm lengths
- The curve peaks at 6.5 cm, where the number of worms is highest (6)

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Task Interpretation

Although no explicit question is stated, based on the graph, we can infer that the task is likely to analyze or interpret the data shown. Common tasks for such a graph include:

1. Finding the most common length (mode)
2. Estimating the range of worm lengths
3. Determining how many worms are in a certain length range
4. Describing the shape of the distribution

Let’s solve and explain each possible interpretation.

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Step-by-Step Analysis

#### 1. Mode (Most Common Length)

The peak of the curve occurs at 6.5 cm, where the number of worms reaches 6.
✔ So, the most common worm length is 6.5 cm.

#### 2. Range of Worm Lengths

- Minimum length: ~4.0 cm (where the curve starts)
- Maximum length: ~9.0 cm (where the curve ends)

✔ So, the range is from 4.0 cm to 9.0 cm.

#### 3. Shape of the Distribution

The curve is symmetrical, bell-shaped, and centered around 6.5 cm.

✔ This indicates a normal distribution (approximately), meaning most worms are close to the average length, with fewer very short or very long worms.

#### 4. Number of Worms at Specific Lengths

We can estimate the number of worms at various lengths by reading the y-values:

| Length (cm) | Number of Worms |
|-------------|------------------|
| 4.0 | 0 |
| 4.5 | 0 |
| 5.0 | 1 |
| 5.5 | 2 |
| 6.0 | 4 |
| 6.5 | 6 (maximum) |
| 7.0 | 4 |
| 7.5 | 2 |
| 8.0 | 1 |
| 8.5 | 0 |
| 9.0 | 0 |

✔ Total number of worms =
1 + 2 + 4 + 6 + 4 + 2 + 1 = 20 worms

(We assume the points represent discrete counts, and the curve is a smooth approximation.)

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Conclusion

Based on the graph:

- The most common worm length is 6.5 cm.
- The distribution is symmetric and bell-shaped, suggesting normality.
- The total number of worms measured is 20.
- The range of lengths is 4.0 cm to 9.0 cm.

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✔ Final Answer:

The data shows that the most common worm length is 6.5 cm, with a total of 20 worms measured across lengths from 4.0 cm to 9.0 cm, forming a symmetrical, bell-shaped distribution.

If you have a specific question (e.g., "What is the mode?" or "How many worms are longer than 7.0 cm?"), feel free to ask!