Mathematics - Statistics Question with Solution | TestHub

Arranging the given data in ascending order

we get,

$\begin{array}{lllllll}{x}_i& 3& 4& 5& 8& 10& 11\\ f_i& 5& 4& 4& 2& 2& 3\end{array}$

Now finding the mean of the above data we get,

Mean $=\frac{3\times 5+8\times 2+11\times 3+10\times 2+5\times 4+4\times 4}{5+2+3+2+4+4}$

$=\frac{15+16+33+20+20+16}{20}=\frac{120}{20}=6$

Now, median $=\frac{1}{2}\left({10}^{\mathrm{th}}+{11}^{\mathrm{th}} \mathrm{observation}\right)$

$=\frac{1}{2}\left(5+5\right)=5$

Hence, Mean deviation about mean will be,

$=\frac{3\times 5+2\times 4+1\times 4+2\times 2+4\times 2+5\times 3}{20}$

$=\frac{54}{20}=2.7$

And Mean deviation about median

$=\frac{2\times 5+1\times 4+0+3\times 2+5\times 2+6\times 3}{20}$

$=\frac{4.8}{20}=2.4$

$P\to 3; Q\to 2; R\to 4; S\to 5$

$\therefore$ Option A is correct.