Question

Diane checked the available memory on 7 computers in the computer lab. The amounts were:
7.3 GB7.2 GB4.7 GB2.6 GB8.0 GB3.0 GB1.5 GB
What was the mean absolute deviation of the amount of memory available?

If the answer is a decimal, round it to the nearest tenth.

mean absolute deviation (MAD):
GB

Answer 1

To calculate the Mean Absolute Deviation (MAD) of the amounts of memory available, follow these steps:

1. **List the amounts of memory**:
- 7.3 GB
- 7.2 GB
- 4.7 GB
- 2.6 GB
- 8.0 GB
- 3.0 GB
- 1.5 GB

2. **Calculate the mean (average)**:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]
Sum of all values:
\[
7.3 + 7.2 + 4.7 + 2.6 + 8.0 + 3.0 + 1.5 = 34.3 \text{ GB}
\]
Number of values = 7.
\[
\text{Mean} = \frac{34.3}{7} \approx 4.91428571 \text{ GB} \quad \text{(approximately 4.9 GB when rounded)}
\]

3. **Calculate the absolute deviations from the mean**:
\[
|7.3 - 4.91428571| \approx 2.38571429
\]
\[
|7.2 - 4.91428571| \approx 2.28571429
\]
\[
|4.7 - 4.91428571| \approx 0.21428571
\]
\[
|2.6 - 4.91428571| \approx 2.31428571
\]
\[
|8.0 - 4.91428571| \approx 3.08571429
\]
\[
|3.0 - 4.91428571| \approx 1.91428571
\]
\[
|1.5 - 4.91428571| \approx 3.41428571
\]

4. **Sum the absolute deviations**:
\[
2.38571429 + 2.28571429 + 0.21428571 + 2.31428571 + 3.08571429 + 1.91428571 + 3.41428571 \approx 15.6
\]

5. **Calculate the Mean Absolute Deviation (MAD)**:
\[
\text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} = \frac{15.6}{7} \approx 2.22857143
\]

6. **Round to the nearest tenth**:
The MAD ≈ 2.2 GB.

Therefore, the Mean Absolute Deviation of the amount of memory available is approximately **2.2 GB**.