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:

Step1: Calculate the mean

First, find the sum of the data points: \(2.5 + 7.4 + 9.3 + 6.1 + 6.6 + 5.9 + 5.6\)
\[

$$\begin{align*} &2.5+7.4 = 9.9\\ &9.9+9.3 = 19.2\\ &19.2+6.1 = 25.3\\ &25.3+6.6 = 31.9\\ &31.9+5.9 = 37.8\\ &37.8+5.6 = 43.4 \end{align*}$$

\]
There are 7 data points, so the mean \(\bar{x}=\frac{43.4}{7} = 6.2\)

Step2: Find the absolute deviations

Calculate \(|x_i - \bar{x}|\) for each data point:

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

Step3: Calculate the mean of these absolute deviations

Sum the absolute deviations: \(3.7 + 1.2 + 3.1 + 0.1 + 0.4 + 0.3 + 0.6\)
\[

$$\begin{align*} &3.7+1.2 = 4.9\\ &4.9+3.1 = 8.0\\ &8.0+0.1 = 8.1\\ &8.1+0.4 = 8.5\\ &8.5+0.3 = 8.8\\ &8.8+0.6 = 9.4 \end{align*}$$

\]
Now, divide by the number of data points (7): \(\text{MAD}=\frac{9.4}{7}\approx1.3\) (rounded to the nearest tenth)

Answer:

\(1.3\)