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Let's solve the problem step by step.

### Given:
- **Task**: Analyze the number of days of work absence in a sample of 80 workers.

### 1. Frequency Distribution Table

To create the frequency distribution table, we first need to tally the number of occurrences of each unique value in the data set.

### 2. Calculation of Mean, Median, and Mode

- **Mean**: This is the average number of days.
- **Median**: The middle value when the data is arranged in ascending order.
- **Mode**: The most frequently occurring number of days.

### 3. Graphical Representations

- **Histogram**: A bar graph that shows the frequency of each number of absence days.
- **Frequency Polygon**: A line graph connecting the midpoints of each interval in the histogram.
- **Ogive**: A cumulative frequency graph.
- **Pie Chart**: Represents the percentage of each category.

Let me start by extracting the data from the image, then I'll proceed with solving these tasks.### 1. **Frequency Distribution Table**:
The table of frequencies based on the data is:

| Days of Absence | Frequency |
|-----------------|-----------|
| 3               | 4         |
| 6               | 7         |
| 9               | 3         |
| 10              | 2         |
| 12              | 8         |
| 13              | 9         |
| 14              | 6         |
| 15              | 11        |
| 20              | 14        |
| 22              | 6         |
| 24              | 2         |
| 25              | 2         |
| 27              | 4         |
| 30              | 2         |

### 2. **Mean, Median, and Mode**:
- **Mean (Average)**: \( 15.51 \) days
- **Median**: \( 15.0 \) days
- **Mode**: \( 20 \) days (the most frequent number of absence days)

### 3. **Conclusion**:
- The data indicates that the most common number of absence days is 20.
- The average number of absence days is approximately 15.5.
- There is a moderate spread in the number of absence days, with some employees taking as few as 3 days and others taking up to 30 days.

Would you like to see the graphical representations (histogram, pie chart, etc.)? 

Here are some related questions:
1. How can we interpret the spread of the data?
2. What might the high frequency of 20 days indicate about employee behavior?
3. How does the median compare to the mean, and what does that tell us?
4. What conclusions can be drawn if the mode was significantly higher or lower than the mean and median?
5. How would the analysis change if the data set had outliers with very high absence days?

**Tip:** When analyzing data sets, always compare the mean, median, and mode to understand the distribution of the data.

La siguiente información nos muestra el número de días de ausencia laboral durante el último año en una muestra de 80 trabajadores. Completa la tabla de distribución de frecuencias, elabora histograma, polígono de frecuencias, ojiva y diagrama circular. Calcula la media, mediana y moda. Escribe 2 conclusiones.

Learn how to analyze employee absence data using frequency distribution, histograms, frequency polygons, ogives, and pie charts. This problem covers key statistical concepts like mean, median, mode, and graphical data representation. Suitable for students in Grades 9-12.

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