Let's go through each question in detail.

Question 7

The question asks for the best strategy to resolve an initial situation.

Options:

• a) Plantear una ecuación (Set up an equation)
• b) El diagrama analógico (Analogous diagram)
• c) El diagrama tabular (Tabular diagram)

To resolve this type of problem, a tabular diagram (Option C) is often effective, as it organizes data in a clear, structured way, making it easier to analyze patterns or find averages, frequencies, and totals, as shown in the following questions.

Answer: Option C (El diagrama tabular).

Question 8

This question requires calculating the arithmetic mean using the data provided in the table. The formula for the mean ($\bar{x}$) is:

$\bar{x} = \frac{\sum_{i=1}^{k} x_i \cdot f_i}{n}$

Where:

• $x_i$ represents each value of "Hora/día" (hours per day),
• $f_i$ represents the frequency of each $x_i$,
• $n$ is the total frequency, which is 30 in this case.

Using the table:

1. Calculate $x_i \cdot f_i$ for each row. The values are given in the table under $x_i \cdot f_i$.
2. Sum these values: $4 + 10 + 15 + 20 + 25 = 74$.
3. Divide this sum by the total frequency (30) to find the mean.

$\bar{x} = \frac{74}{30} \approx 2.47$

Thus, the mean number of hours per day is approximately 2.47 hours.

Would you like a more detailed breakdown of any of the steps?

Here are five questions to deepen your understanding:

1. How would the process change if the frequencies were not whole numbers?
2. Why is the tabular method effective for calculating means with grouped data?
3. How would you interpret the mean in the context of daily hours?
4. What would be the impact of adding another row with higher hours and frequency?
5. How can this method be applied to other types of statistical data?

Tip: For frequency distributions, organizing your data in a tabular format makes calculations like the mean, median, and mode much easier and more accurate.