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In this exercise, you are asked to match each histogram (a, b, c, d) with its corresponding box plot (1, 2, 3, 4). Here's how to approach the problem:

### Step-by-step Guide:

1. **Histogram Analysis**:
   - A histogram provides a visual representation of data distribution, showing how often values fall into different intervals (bins). The shape of the histogram (e.g., skewness or symmetry) gives us clues about the data's central tendency, variability, and distribution.

2. **Box Plot Analysis**:
   - A box plot (or box-and-whisker plot) represents data distribution through five summary statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. 
   - It helps in identifying skewness and spread of the data. Outliers are also often marked.

3. **Matching Histograms to Box Plots**:
   - **Histogram a** shows a **right-skewed distribution**, meaning the tail extends to the right. This suggests that the median will be closer to Q1, with a longer whisker on the right side in the box plot. **Box plot (1)** likely matches this pattern.
   - **Histogram b** is **left-skewed**, meaning the tail extends to the left. This indicates that the median will be closer to Q3, and there will be a longer whisker on the left side. **Box plot (2)** is a good match.
   - **Histogram c** is also **right-skewed**, similar to (a) but with a less pronounced tail. **Box plot (3)** shows this with a smaller degree of skewness.
   - **Histogram d** appears to be **symmetrical**, with no significant skewness. **Box plot (4)** represents this symmetry since the whiskers are balanced on both sides.

### Final Matches:
- Histogram a → Box plot (1)
- Histogram b → Box plot (2)
- Histogram c → Box plot (3)
- Histogram d → Box plot (4)

Would you like further explanation on any part, or would you like to ask a specific question? Here are some related questions you might find helpful:

1. How can you identify skewness from a histogram?
2. What specific features of a box plot indicate data spread?
3. What is the relationship between quartiles and histogram shapes?
4. How do outliers affect the appearance of a box plot?
5. Can a symmetric histogram always correspond to a symmetric box plot?

**Tip**: A right-skewed distribution has a longer right tail, while a left-skewed distribution has a longer left tail. Keep this in mind when matching histograms to box plots.

Relacione cada histograma con el diagrama de caja que representa el mismo conjunto de datos.

Learn how to match histograms with their corresponding box plots by analyzing data distribution, skewness, and spread. This problem covers essential statistical concepts such as skewness, quartiles, and the relationship between histograms and box plots. Suitable for students in Grades 10-12.

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