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: \(2.5 + 7.4 + 9.3 + 6.1 + 6.6 + 5.9 + 5.6\)

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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: \(3.7 + 1.2 + 3.1 + 0.1 + 0.4 + 0.3 + 0.6\)

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

Answer:

\(1.3\)