Question

nana measures the lengths of mice. their lengths, in centimeters, are recorded. there are 10 values. 7 12 8.5 11 6.5 9 12 7 10 6 what is the mean absolute deviation of the data set? enter the value to the nearest tenth. centimeters

Explanation:

Step1: Calculate the mean

The data set is \(7, 12, 8.5, 12, 7, 11, 6.5, 9, 10, 6\). The sum of the data values is \(7 + 12+8.5 + 12+7+11+6.5+9+10+6=89\). The mean \(\bar{x}=\frac{89}{10} = 8.9\).

Step2: Calculate the absolute - deviations

For \(7\): \(|7 - 8.9|=1.9\); for \(12\): \(|12 - 8.9| = 3.1\); for \(8.5\): \(|8.5 - 8.9|=0.4\); for \(12\): \(|12 - 8.9| = 3.1\); for \(7\): \(|7 - 8.9|=1.9\); for \(11\): \(|11 - 8.9| = 2.1\); for \(6.5\): \(|6.5 - 8.9|=2.4\); for \(9\): \(|9 - 8.9|=0.1\); for \(10\): \(|10 - 8.9| = 1.1\); for \(6\): \(|6 - 8.9|=2.9\).

Step3: Calculate the mean of the absolute - deviations

The sum of the absolute - deviations is \(1.9+3.1 + 0.4+3.1+1.9+2.1+2.4+0.1+1.1+2.9 = 18.9\). The mean absolute deviation \(MAD=\frac{18.9}{10}=1.89\approx1.9\).

Answer:

\(1.9\)