Question

1. what is the mean absolute deviation of the data set: 5, 8, 8, 9, 10?

Explanation:

Step1: Calculate the mean

The data set is \(5, 8, 8, 9, 10\). The mean \(\bar{x}\) is calculated as \(\frac{5 + 8 + 8 + 9 + 10}{5}\).

$$ \frac{5 + 8 + 8 + 9 + 10}{5}=\frac{40}{5} = 8 $$

Step2: Find absolute deviations

For each data point, find \(|x - \bar{x}|\):

• For \(x = 5\): \(|5 - 8|= 3\)
• For \(x = 8\): \(|8 - 8|= 0\)
• For \(x = 8\): \(|8 - 8|= 0\)
• For \(x = 9\): \(|9 - 8|= 1\)
• For \(x = 10\): \(|10 - 8|= 2\)

Step3: Calculate the mean of absolute deviations

Sum the absolute deviations: \(3 + 0 + 0 + 1 + 2 = 6\). Divide by the number of data points (\(5\)): \(\frac{6}{5}=1.2\).

Answer:

\(1.2\)