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To calculate the "Desvio Médio Simples" (Mean Absolute Deviation) for the given data set, we need to follow these steps:

1. **Compute the Mean**:
   First, we need to calculate the mean (\(\bar{x}\)) of the data set, where:
   \[
   \bar{x} = \frac{\sum (x_i \cdot f_i)}{\sum f_i}
   \]
   Here, \(x_i\) are the values and \(f_i\) are their respective frequencies.

2. **Calculate the Deviations**:
   For each value \(x_i\), compute the absolute deviation from the mean \(|x_i - \bar{x}|\).

3. **Multiply by the Frequencies**:
   Multiply each absolute deviation by its respective frequency.

4. **Calculate the Mean of the Absolute Deviations**:
   Finally, the Mean Absolute Deviation is given by:
   \[
   \text{Mean Absolute Deviation} = \frac{\sum (f_i \cdot |x_i - \bar{x}|)}{\sum f_i}
   \]

Let's compute these steps now.

The data is:
\[
x_i = [2, 3, 4, 7, 10, 11], \quad f_i = [2, 3, 5, 7, 5, 4]
\]

### Step 1: Calculate the Mean
\[
\bar{x} = \frac{(2 \cdot 2) + (3 \cdot 3) + (4 \cdot 5) + (7 \cdot 7) + (10 \cdot 5) + (11 \cdot 4)}{2 + 3 + 5 + 7 + 5 + 4}
\]

I will now calculate this value.The mean (\(\bar{x}\)) of the data is approximately \(6.77\).

### Step 2: Calculate the Absolute Deviations
Now, we will compute the absolute deviations \(|x_i - \bar{x}|\) for each value, multiply them by the frequencies, and then compute the mean of these absolute deviations. Let's move to the next steps.The Mean Absolute Deviation (Desvio Médio Simples) for the given data is approximately \(2.67\).

The correct option is the first one: **2.67**.

Would you like more details on the calculation or any specific step?

Here are 5 related questions you could explore:
1. How does the mean absolute deviation differ from standard deviation?
2. What are other ways to measure data dispersion besides the mean absolute deviation?
3. How would the calculation change if there were outliers in the data?
4. What is the significance of frequency in this type of problem?
5. How can mean absolute deviation be applied in real-world data analysis?

**Tip**: When dealing with large data sets, organizing your data in a table helps avoid errors during calculations.

O valor do Desvio Médio Simples para a distribuição abaixo é?

Learn how to calculate the Mean Absolute Deviation (Desvio Médio Simples) for the given frequency distribution table. Includes step-by-step instructions on computing the mean and deviations. Suitable for students in Grades 10-12.

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