which box plot represents a symmetrically distributed data set
A box plot (box-and-whisker plot) represents a **symmetrically distributed dataset** if it meets the following criteria:
**Key Features of a Symmetric Box Plot**
1. **Median Position**
- The median (middle line inside the box) is **exactly centered** between the first quartile (Q1, lower edge of the box) and the third quartile (Q3, upper edge of the box).
- **Mathematically**:
*(Source: Wikimedia Commons)*
- **Symmetric characteristics**:
- Median is centered in the box.
- Whiskers are balanced.
- No skewness (data spreads equally on both sides of the median).
**Asymmetric Box Plots (for Comparison)**
| Type | Box Plot Feature | Distribution |
| Right-Skewed | Median is closer to Q1; upper whisker is longer. | Tail on the right. |
| Left-Skewed | Median is closer to Q3; lower whisker is longer. | Tail on the left. |
**How to Identify Symmetry**
1. **Visual Check**
- If the box plot looks **mirror-symmetric** around the median, the data is symmetric.
2. **Statistical Check**
- Calculate the **skewness** (should be close to 0 for symmetric data).
**Answer**
Choose the box plot where:
1. The median is **centered** in the box.
2. The whiskers are **balanced** in length.
3. There is **no obvious skewness** (no long tail on one side).
