Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
The given data is
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Mean of the given data,
\(\bar{x}=\frac{38+70+48+40+42+55+63+46+54+44}{10}=\frac{500}{10}=50\)
The deviations of the respective observations from the mean \(\bar{x},i.e.x_i-\bar{x}\) are
12, 20, 2, 10, 8, 5, 13, 4, 4, 6
The absolute values of the deviations, i.e. \(|x_i-\bar{x}|\), are
12, 20, 2, 10, 8, 5, 13, 4, 4, 6
The required mean deviation about the mean is \(M.D(\bar{x})=\frac{\sum_{i=1}^{8}|x_i-\bar{x}|}{10}\)
\(=\frac{12+20+2+10+8+5+13+4+4+6}{10}\)
\(=\frac{84}{10}\)
\(=8.4\)