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resuleve el problema empleando la tabla de estadistica

To solve the problem using the provided statistical tables, we'll follow these steps:

### 1. **Identify the Samples:**
   - **Muestra de Ángela:** \( 14, 13, 16, 17, 18, 19, 20, 22, 23, 25, 27, 28 \)
   - **Muestra de Consuelo:** \( 18, 19, 19, 21, 22, 23, 24, 26, 27, 28, 30, 41 \)

### 2. **Calculate the Measures of Dispersion:**

   #### **Range (Rango):**
   - **Angela:** \( R_A = \text{Max} - \text{Min} = 28 - 13 = 15 \)
   - **Consuelo:** \( R_C = \text{Max} - \text{Min} = 41 - 18 = 23 \)

   #### **Variance (Varianza):**
   The variance is calculated as:
   \[
   \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2
   \]
   - **Angela:** 
     \[
     \text{Mean} (\mu_A) = \frac{\sum x_i}{12} = \frac{242}{12} \approx 20.17
     \]
     \[
     \sigma^2_A = \frac{1}{12} \left[(14-20.17)^2 + \dots + (28-20.17)^2 \right] \approx 25.14
     \]
   - **Consuelo:** 
     \[
     \text{Mean} (\mu_C) = \frac{\sum x_i}{12} = \frac{298}{12} \approx 24.83
     \]
     \[
     \sigma^2_C = \frac{1}{12} \left[(18-24.83)^2 + \dots + (41-24.83)^2 \right] \approx 44.68
     \]

   #### **Standard Deviation (Desviación Estándar):**
   \[
   \sigma = \sqrt{\sigma^2}
   \]
   - **Angela:** 
     \[
     \sigma_A \approx \sqrt{25.14} \approx 5.01
     \]
   - **Consuelo:** 
     \[
     \sigma_C \approx \sqrt{44.68} \approx 6.68
     \]

   #### **Coefficient of Variation (Coeficiente de Variación):**
   \[
   CV = \frac{\sigma}{\mu} \times 100\%
   \]
   - **Angela:**
     \[
     CV_A \approx \frac{5.01}{20.17} \times 100\% \approx 24.83\%
     \]
   - **Consuelo:**
     \[
     CV_C \approx \frac{6.68}{24.83} \times 100\% \approx 26.90\%
     \]

### 3. **Interpretation:**
   - The **range** shows that Consuelo's sample is more spread out than Angela's.
   - The **variance** and **standard deviation** confirm that Consuelo's data is more dispersed.
   - The **coefficient of variation** indicates that relative to the mean, Consuelo's data has slightly more variability than Angela's.

Would you like more detailed calculations or have any questions about these results?

### Relative Questions:
1. How does the coefficient of variation help in comparing the variability of two datasets?
2. What does a higher standard deviation imply about a dataset?
3. How would the results change if an outlier was introduced in Angela's data?
4. Why is it important to consider both variance and standard deviation?
5. How could this analysis be extended to larger datasets?

### Tip:
When comparing datasets with different means, the coefficient of variation is a useful tool as it provides a normalized measure of dispersion.

Explore statistical analysis using sample data from Angela and Consuelo. Calculate measures of dispersion such as range, variance, standard deviation, and coefficient of variation to compare the variability of the datasets. Detailed step-by-step solution provided.

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