Question

tina checked the available memory on 7 computers in the computer lab. the amounts were:
2.5 gb 7.4 gb 9.3 gb 6.1 gb 6.6 gb 5.9 gb
5.6 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

Explanation:

Step 1: Calculate the mean

First, we find the mean (\(\bar{x}\)) of the data set. The data points are \(2.5, 7.4, 9.3, 6.1, 6.6, 5.9, 5.6\). The sum of these values is:

$$ 2.5 + 7.4 + 9.3 + 6.1 + 6.6 + 5.9 + 5.6 = 43.4 $$

There are 7 data points, so the mean is:

$$ \bar{x} = \frac{43.4}{7} = 6.2 $$

Step 2: Find the absolute deviations

Next, we find the absolute deviation of each data point from the mean. The absolute deviation is \(|x - \bar{x}|\) for each \(x\):

• \(|2.5 - 6.2| = 3.7\)
• \(|7.4 - 6.2| = 1.2\)
• \(|9.3 - 6.2| = 3.1\)
• \(|6.1 - 6.2| = 0.1\)
• \(|6.6 - 6.2| = 0.4\)
• \(|5.9 - 6.2| = 0.3\)
• \(|5.6 - 6.2| = 0.6\)

Step 3: Calculate the mean of the absolute deviations

Now, we find the mean of these absolute deviations. The sum of the absolute deviations is:

$$ 3.7 + 1.2 + 3.1 + 0.1 + 0.4 + 0.3 + 0.6 = 9.4 $$

The mean absolute deviation (MAD) is the sum of the absolute deviations divided by the number of data points:

$$ \text{MAD} = \frac{9.4}{7} \approx 1.3 $$

Answer:

\(1.3\)