Question

he hours students reported practicing their instruments last grading quarter were 29, 20, 36, 44, 30, 32, and 40.

The mean hours students reported practicing their instruments is
.

The mean absolute deviation for the data is
.

Answer 1

To find the mean and the mean absolute deviation (MAD) for the given data:

### Step 1: Calculate the Mean

The formula for the mean is:

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]

**Given Data:**
- Hours reported: 29, 20, 36, 44, 30, 32, 40

**Calculate the sum:**
\[
29 + 20 + 36 + 44 + 30 + 32 + 40 = 231
\]

**Number of values:**
There are 7 values.

**Calculate the mean:**
\[
\text{Mean} = \frac{231}{7} = 33
\]

### Step 2: Calculate the Mean Absolute Deviation (MAD)

The formula for the mean absolute deviation is:

\[
\text{MAD} = \frac{\sum |x_i - \text{Mean}|}{n}
\]

Where \( x_i \) are the data points, and \( n \) is the number of data points.

**Calculate the absolute deviations from the mean:**
Mean = 33

- \( |29 - 33| = 4 \)
- \( |20 - 33| = 13 \)
- \( |36 - 33| = 3 \)
- \( |44 - 33| = 11 \)
- \( |30 - 33| = 3 \)
- \( |32 - 33| = 1 \)
- \( |40 - 33| = 7 \)

**Sum of the absolute deviations:**
\[
4 + 13 + 3 + 11 + 3 + 1 + 7 = 42
\]

**Calculate the MAD:**
\[
\text{MAD} = \frac{42}{7} = 6
\]

### Summary:
- The mean hours students reported practicing their instruments is **33**.
- The mean absolute deviation for the data is **6**.