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To calculate the mean absolute deviation (MAD) for the given set of numbers, follow these steps:

**Numbers:**
\[ 32, 43, 18, 28, 51 \]

### Step 1: Calculate the Mean
First, we need to find the mean of the numbers.

\[
\text{Mean} = \frac{32 + 43 + 18 + 28 + 51}{5} = \frac{172}{5} = 34.4
\]

### Step 2: Find the Absolute Deviations
Next, we calculate the absolute deviation of each number from the mean.

\[
\begin{aligned}
|32 - 34.4| &= 2.4 \\
|43 - 34.4| &= 8.6 \\
|18 - 34.4| &= 16.4 \\
|28 - 34.4| &= 6.4 \\
|51 - 34.4| &= 16.6 \\
\end{aligned}
\]

### Step 3: Calculate the Mean of the Absolute Deviations
Finally, find the mean of these absolute deviations:

\[
\text{MAD} = \frac{2.4 + 8.6 + 16.4 + 6.4 + 16.6}{5} = \frac{50.4}{5} = 10.08
\]

It seems like none of the options match this exact value. There could be a typo in the options, but the correct **mean absolute deviation (MAD)** is **10.08**.

Would you like more details, or have any further questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate the standard deviation of a data set?
2. What is the significance of the mean absolute deviation in statistics?
3. How does the MAD differ from variance and standard deviation?
4. What are some real-world applications of the mean absolute deviation?
5. How do changes in data affect the MAD of a data set?

**Tip:** When comparing variability, mean absolute deviation is simpler to interpret but less sensitive to extreme values than standard deviation.

The list shows the number of songs that five students each downloaded last week. 32, 43, 18, 28, 51. What is the mean absolute deviation of the numbers in the list?

Calculate the mean absolute deviation (MAD) for the number of songs downloaded by five students: 32, 43, 18, 28, and 51. Step-by-step explanation covering calculation of the mean, absolute deviations, and MAD.

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