Question

find a. the mean, b. the deviation from the mean for each data item, and c. the sum of the deviations in part (b) for the following group of data items: 133, 139, 144, 146, 148. a. the mean is . (simplify your answer.) b. complete the following table by entering the deviations for each data value. data item deviation 133 139 144 146 148 (simplify your answers.) c. the sum of the deviations is . (simplify your answer.)

Explanation:

Step1: Calculate the mean

The data set is \(133, 139, 144, 146, 148\). The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 5\), \(x_1=133\), \(x_2 = 139\), \(x_3=144\), \(x_4=146\), \(x_5=148\).
\(\bar{x}=\frac{133 + 139+144+146+148}{5}=\frac{710}{5}=142\)

Step2: Calculate the deviations

For \(x_1 = 133\), the deviation \(d_1=133 - 142=-9\)
For \(x_2 = 139\), the deviation \(d_2=139 - 142=-3\)
For \(x_3 = 144\), the deviation \(d_3=144 - 142 = 2\)
For \(x_4 = 146\), the deviation \(d_4=146 - 142 = 4\)
For \(x_5 = 148\), the deviation \(d_5=148 - 142 = 6\)

Step3: Calculate the sum of the deviations

\(d_1 + d_2+d_3+d_4+d_5=-9+( - 3)+2 + 4+6=0\)

Answer:

a. \(142\)
b. \(-9,-3,2,4,6\)
c. \(0\)