Question

The number of boxes of food that six volunteers collected for the food drive is given in the table below.

Number of Boxes
32
35
20
16
28
13


What is the mean absolute deviation? Round to the nearest tenth.

Answer 1

To calculate the mean absolute deviation (MAD), follow these steps:

1. **Calculate the mean (average)** of the data set.
2. **Find the absolute deviation** from the mean for each data point.
3. **Calculate the mean of these absolute deviations**.

### Step 1: Calculate the Mean
First, sum up the number of boxes collected:

\[
32 + 35 + 20 + 16 + 28 + 13 = 144
\]

Next, divide by the number of data points (which is 6):

\[
\text{Mean} = \frac{144}{6} = 24
\]

### Step 2: Calculate the Absolute Deviations
Now, find the absolute deviation of each value from the mean (24):

- |32 - 24| = 8
- |35 - 24| = 11
- |20 - 24| = 4
- |16 - 24| = 8
- |28 - 24| = 4
- |13 - 24| = 11

### Step 3: Calculate the Mean of Absolute Deviations
Now sum the absolute deviations:

\[
8 + 11 + 4 + 8 + 4 + 11 = 46
\]

Then, divide by the number of data points (which is 6):

\[
\text{Mean Absolute Deviation} = \frac{46}{6} \approx 7.6667
\]

### Final Result
Rounding to the nearest tenth, the mean absolute deviation is:

\[
\text{Mean Absolute Deviation} \approx 7.7
\]

Thus, the mean absolute deviation is **7.7**.