Question

Find the mean deviation about the mean for the following data :
$12$, $3$, $18$, $17$, $4$, $9$, $17$, $19$, $20$, $15$, $8$, $17$, $2$, $3$, $16$, $11$, $3$, $1$, $0$, $5$

• A. $8.2$
• B. $9.2$
• C. $6.2$
• D. $5.2$

Answer 1

Answer: (C)

The mean $(\bar{x})$ of the given data is,
$\bar{x} = \frac{1}{20} \sum\limits^{20}_{i = 1} x_{i} = \frac{200}{20} = 10$
The values of the deviations from mean, i.e., $\left|x_{i}-\bar{x}\right|$ are
$2$, $7$, $8$, $7$, $6$, $1$, $7$, $9$, $10$, $5$, $2$, $7$, $8$, $7$, $6$, $1$, $7$, $9$, $10$, $5$
$\therefore \sum\limits^{20}_{i = 1} \left|x_{i}-\bar{x}\right|= 124$ and $M.D. \left(\bar{x}\right)$
$= \frac{124}{20}=6.2$