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La talla de calzado que mas se vende en los almacenes de Portoviejo, se indican en la siguiente tabla.

Calcule la moda.

a.
36,99


b.
36,78


c.
40,15


d.
38,25

Let's recalculate the mode using the details provided and confirm the correct answer from the given options.

### Recalculation of the Mode

Given table:

\[
\begin{array}{|c|c|c|c|}
\hline
\text{Talla (x)} & \text{Punto Medio (xm)} & \text{Frecuencia (fi)} & \text{Frecuencia Acumulada (Fi)} \\
\hline
27 - 30 & 28.5 & 75 & 75 \\
30 - 33 & 31.5 & 38 & 113 \\
33 - 36 & 34.5 & 32 & 145 \\
36 - 39 & 37.5 & 80 & 225 \\
39 - 42 & 40.5 & 64 & 289 \\
\hline
\end{array}
\]

### Steps to Calculate the Mode:
1. **Identify the modal class**: 
   - The class with the highest frequency is **36 - 39**, with \(f_1 = 80\).
2. **Use the mode formula**: 
   \[
   \text{Mode} = L + \left( \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \right) \times h
   \]
   Where:
   - \(L = 36\) (lower boundary of the modal class)
   - \(f_1 = 80\) (frequency of the modal class)
   - \(f_0 = 32\) (frequency of the class before the modal class)
   - \(f_2 = 64\) (frequency of the class after the modal class)
   - \(h = 3\) (width of each class interval)

### Substituting Values:

\[
\text{Mode} = 36 + \left( \frac{80 - 32}{(2 \times 80) - 32 - 64} \right) \times 3
\]

\[
\text{Mode} = 36 + \left( \frac{48}{160 - 96} \right) \times 3
\]

\[
\text{Mode} = 36 + \left( \frac{48}{64} \right) \times 3
\]

\[
\text{Mode} = 36 + 0.75 \times 3 = 36 + 2.25
\]

\[
\text{Mode} = 38.25
\]

### Conclusion:
The mode is **38.25**, which corresponds to option **d**.

Would you like to explore more details on this topic or have any other questions? Here are some related questions to consider:

1. How does the mode compare with the mean in this distribution?
2. Could there be more than one mode in a different data set? How would that affect the analysis?
3. What is the significance of the modal value in business decisions related to inventory management?
4. How does the class width impact the accuracy of the mode?
5. What other statistical measures can be derived from this frequency distribution?

**Tip:** In real-life applications, the mode is particularly useful in inventory management and marketing, as it represents the most popular item or product size, helping businesses focus on the most demanded items.

Learn how to calculate the mode for shoe sizes sold in Portoviejo stores using a detailed step-by-step solution. This problem involves statistical analysis and applies the mode formula for grouped data. Find out the most frequently sold shoe size accurately!

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