Question

The mean deviation from mean of observations 5, 10, 15, 20, ......85 is

• A. $43.71$
• B. $21.17$
• C. $38.7$
• D. None of these

Answer 1

Answer: (B)

$21.17$

Given series is $5,10,15,....,85$, which is an AP.
Last term $85=a+(n-1)d$
$\Rightarrow n=17$
Sum of $n$ terms of AP $=\frac{17}{2}(5+85)$
$\sum x_i=765$
$\overline{x}=\frac{\sum x_i}{n}$
$\overline{x}=\frac{765}{17}=45$
So, deviations from mean are $40,35,25,20,15,10,5,0,5,10,15,20,25,30,35,40$
Sum of deviations $=360$
Mean deviation from mean $=\frac{360}{17}=21.17$