Question

Students reported practicing violin during the last semester for 45, 38, 52, 58, and 42 hours. What is the mean absolute deviation for the number of hours students practiced the violin? Round to the nearest tenth.
6.4
6.8
32
47

Answer 1

To find the mean absolute deviation (MAD) of the number of hours students practiced the violin, we follow these steps:

1. Calculate the mean (average) of the data set.
2. Find the absolute deviations from the mean.
3. Calculate the mean of these absolute deviations.

Let's start with the data set: 45, 38, 52, 58, and 42 hours.

### Step 1: Calculate the Mean
The mean is calculated as follows:

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{45 + 38 + 52 + 58 + 42}{5}
\]

Calculating the sum:

\[
45 + 38 + 52 + 58 + 42 = 235
\]

Now, divide by the number of values (5):

\[
\text{Mean} = \frac{235}{5} = 47
\]

### Step 2: Calculate the Absolute Deviations
Now, we calculate the absolute deviations from the mean (47):

\[
|45 - 47| = 2
\]
\[
|38 - 47| = 9
\]
\[
|52 - 47| = 5
\]
\[
|58 - 47| = 11
\]
\[
|42 - 47| = 5
\]

The absolute deviations are: 2, 9, 5, 11, and 5.

### Step 3: Calculate the Mean of Absolute Deviations
Now we calculate the mean of these absolute deviations:

\[
\text{Mean Absolute Deviation} = \frac{2 + 9 + 5 + 11 + 5}{5}
\]

Calculating the sum of absolute deviations:

\[
2 + 9 + 5 + 11 + 5 = 32
\]

Now, divide by the number of values (5):

\[
\text{Mean Absolute Deviation} = \frac{32}{5} = 6.4
\]

### Conclusion
The mean absolute deviation for the number of hours students practiced the violin is **6.4**.