which box plot represents a symmetrically distributed data set

A box plot representing a **symmetrically distributed data set** will have the following characteristics:

**Key Features of a Symmetric Box Plot**

1. **Median in the center of the box**  

   - The line inside the box (**median, Q2**) is exactly halfway between the **first quartile (Q1)** and **third quartile (Q3)**.  

   - Mathematically:  

     **Q2 − Q1 = Q3 − Q2**  

     *(The "box" is symmetric around the median)*.

2. **Symmetric whiskers**  

   - The lengths of the **upper whisker** (from Q3 to the maximum) and **lower whisker** (from Q1 to the minimum) are approximately equal.  

   - Mathematically:  

     **Q3 − Q1 ≈ Max − Min**  

     *(No significant skewness in the tails)*.

3. **No outliers disrupting symmetry**  

   - If outliers exist, they are balanced on both sides (optional, as symmetry focuses on the central 50% of data).

 **Example of a Symmetric Box Plot**  

  

- **Box**: Centered at the median, with equal distance from Q1 and Q3.  

- **Whiskers**: Equal length above and below the box.

 **How to Identify Asymmetric Box Plots**  

 **Answer**  

Choose the box plot where:  

1. The **median is centered in the box**, and  

2. The **whiskers are approximately equal in length**.  

This symmetry indicates the data is evenly distributed around the median. ，