A pediatrician took a random sample of 13 children between the ages of 0 and 24 months and measured the number of words that they had in their vocabulary. The data that the pediatrician collected is given in the table.

Age (in months)	Number of Words
1	0
3	0
6	0
9	0
11	1
12	2
15	11
17	42
18	49
20	95
21	100
22	127
24	200

Part A: Would a scatter plot or line graph be more appropriate for displaying and describing the relationship between the age and the number of vocabulary words? Explain your reasoning. (4 points)

Part B: If you were to add an outlier to the graph, describe the data point and what it represents in the real-world situation. (4 points)

Part C: Describe the type and degree of association between age and number of vocabulary words. (4 points)

### Part A: Appropriate Graph for Displaying Data

A scatter plot would be more appropriate for displaying and describing the relationship between the age and the number of vocabulary words. This is because:

1. **Nature of Data**: The data involves two continuous variables (age and number of words) which are best represented by individual points on a graph.
2. **Relationship Visualization**: A scatter plot allows for the visualization of the correlation between the variables, showing how the number of vocabulary words changes with age.
3. **Outlier Detection**: It is easier to identify any outliers or anomalies in the data with a scatter plot.
4. **Trend Identification**: While a line graph connects data points and is useful for showing trends over time, a scatter plot is better for identifying the precise relationship between two variables without implying continuity between data points.

### Part B: Adding an Outlier

An outlier in this context would be a data point that does not follow the trend observed in the rest of the data. For example, a possible outlier could be:

- Age: 10 months
- Number of Words: 50

This data point would represent a child who, at 10 months, has an unusually high vocabulary for their age compared to other children in the sample. In a real-world situation, this could indicate a child with advanced language development or possibly a recording error.

### Part C: Type and Degree of Association

The type of association between age and the number of vocabulary words is positive, as older children tend to have a larger vocabulary. The degree of association appears to be strong, especially from 15 months onwards, where there is a noticeable increase in the number of words with increasing age. This indicates that as children grow older, their vocabulary expands significantly.

#### Scatter Plot of the Data

I will now create a scatter plot to visually represent the relationship between age and the number of vocabulary words.

Let's generate the scatter plot:

```python
import matplotlib.pyplot as plt

# Data
age = [1, 3, 6, 9, 11, 12, 15, 17, 18, 20, 21, 22, 24]
words = [0, 0, 0, 0, 1, 2, 11, 42, 49, 95, 100, 127, 200]

# Plotting the scatter plot
plt.figure(figsize=(10, 6))
plt.scatter(age, words, color='blue', marker='o')
plt.title('Scatter Plot of Age vs. Number of Vocabulary Words')
plt.xlabel('Age (in months)')
plt.ylabel('Number of Vocabulary Words')
plt.grid(True)
plt.show()
```

Would you like more details or have any questions?

Here are five more questions you can ask:
1. How do you calculate the correlation coefficient for this data?
2. What other types of graphs can represent this data effectively?
3. Can you explain how to fit a regression line to this scatter plot?
4. What statistical tests can be used to analyze the significance of the relationship?
5. How can outliers affect the interpretation of the data?

**Tip:** Always look at the scatter plot before fitting any model to understand the distribution and potential outliers in the data.

Explore the relationship between age and vocabulary words in children aged 0-24 months through a scatter plot analysis. Learn why a scatter plot is appropriate for this data, how outliers can impact interpretation, and the type and strength of association observed. Ideal for students and researchers interested in statistics and data visualization.

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