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The problem provided involves calculating the variance of a dataset that represents the minutes consumed by mobile phone customers. The dataset consists of the following values:

\[ 348, 355, 355, 355, 363, 364, 367, 369, 370, 378, 378, 380, 386, 387, 391, 392, 399, 414, 416, 433 \]

The formula for the sample variance \( S^2 \) is given by:

\[
S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2
\]

Where:
- \( n \) is the number of data points
- \( x_i \) is each data point
- \( \overline{x} \) is the mean of the data points

Let's calculate the variance of this dataset. I'll compute the mean, the squared deviations, and then determine the sample variance.The calculated sample variance of the given dataset is approximately \( S^2 = 516.5 \).

Thus, the correct answer is \( S^2 = 516.5 \).

Would you like further clarification or details on how this calculation was done? Here are some related questions to deepen your understanding:

1. How is the standard deviation related to variance?
2. What is the difference between population variance and sample variance?
3. How would the variance change if we had more data points?
4. What are some real-world applications of variance in statistics?
5. How does variance help in understanding the spread of data?

**Tip:** Variance gives you insight into how spread out your data is around the mean, but always check if you are using sample variance or population variance, as they differ by a small factor.

SunCom estudia la cantidad de minutos que consumen sus clientes que cuentan con cierto plan tarifario de telefonía celular. Una muestra aleatoria revela que los minutos consumidos el mes pasado son: [348, 355, 355, 355, 363, 364, 367, 369, 370, 378, 378, 380, 386, 387, 391, 392, 399, 414, 416, 433]. La varianza del consumo de minutos es:

Learn how to calculate the sample variance for the mobile minutes consumed by SunCom's customers using the dataset: [348, 355, 355, 355, 363, 364, 367, 369, 370, 378, 378, 380, 386, 387, 391, 392, 399, 414, 416, 433]. This detailed explanation covers key statistical concepts and the sample variance formula. Suitable for students in Grades 10-12.

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