Question

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is

Options

• 2    

•  2.57       

•  3        

•  3.57 

Answer 1

The given observations are 3, 10, 10, 4, 7, 10, 5.

∴ Mean,  \[x = \frac{3 + 10 + 10 + 4 + 7 + 10 + 5}{7} = \frac{49}{7} = 7\]

Now,

Mean deviation from mean, MD

\[= \frac{\sum_{} \left| x_i - 7 \right|}{7}\]

\[= \frac{\left| 3 - 7 \right| + \left| 10 - 7 \right| + \left| 10 - 7 \right| + \left| 4 - 7 \right| + \left| 7 - 7 \right| + \left| 10 - 7 \right| + \left| 5 - 7 \right|}{7}\]
\[ = \frac{4 + 3 + 3 + 3 + 0 + 3 + 2}{7}\]
\[ = \frac{18}{7}\]
\[ = 2 . 57\]