Visualizing Titanic Passenger Fare Trends with Interpolation

A company wants to analyze the ticket fares of passengers on the Titanic. They have a dataset containing details about each passenger, including their fare prices. However, some fare values are missing. The goal is to visualize the fare trends across passengers while handling the missing values effectively.

### **Solution**  

To solve this, we create an interactive line chart that displays how fares change across passengers. The steps are as follows:  

1. **Load the Titanic Dataset** – The dataset includes passenger details such as age, class, and fare.  

2. **Extract Relevant Data** – We focus on the fare column and use the passenger index for the x-axis.  

3. **Handle Missing Values** – To ensure a smooth trend line, missing fares are filled using interpolation, which estimates missing values based on nearby data points.  

4. **Create a Line Chart** – The fare values are plotted on the y-axis, with the passenger index on the x-axis.  

5. **Make it Interactive** – Using Plotly, we generate an interactive visualization that allows zooming and hovering over data points for details.  

This solution helps analyze fare trends while ensuring missing values do not disrupt the visualization.

Methods for Handling Missing GRE Scores in Admission Datasets

When dealing with missing values in the GRE score column of an admission dataset, there are several practical methods to consider. Each method has its own pros and cons:

1. **Mean Imputation**:

   - **Pros**: Simple to implement and understand; preserves the overall distribution of the data if the missingness is random.

   - **Cons**: Can distort the data if the missingness is not random; does not account for potential relationships with other variables.

2. **Median Imputation**:

   - **Pros**: More robust than mean imputation, especially if the GRE scores are skewed or have outliers; less sensitive to extreme values.

   - **Cons**: Like mean imputation, it doesn’t consider relationships with other variables and might not reflect variability in the data.

3. **Mode Imputation**:

   - **Pros**: Useful if the GRE scores are categorical or if there are repeated scores; can preserve the mode of the data.

   - **Cons**: Not ideal for continuous variables with a wide range; may not be representative if the mode is not indicative of the overall distribution.

4. **Predictive Imputation (e.g., using a regression model)**:

   - **Pros**: Can account for relationships between the GRE score and other variables; potentially more accurate than simple imputation methods.

   - **Cons**: More complex to implement and requires a model to be trained; can introduce bias if the model is not well-specified.

5. **K-Nearest Neighbors (KNN) Imputation**:

   - **Pros**: Considers the similarity between instances; can capture relationships between variables and fill missing values based on similar records.

   - **Cons**: Computationally intensive, especially with large datasets; sensitive to the choice of `k` and the distance metric used.

Choosing the best method depends on the nature of your dataset and the underlying reasons for the missing values. If missingness is random, simpler methods like mean or median imputation might suffice. For more complex patterns, predictive or KNN imputation might be more appropriate.