Consider the given data with frequency distribution | $x_i$ | 3 | 8 | 11 | 10 | 5 | 4 | | --- | --- | --- | --- | --- | --- | --- | | $f_i$ | 5 | 2 | 3 | 2 | 4 | 4 | Match each entry in List-I to the correct entries in List-II. | List-I | List-II | | --- | --- | | (P) The mean of the above data is | (1) 2.5 | | (Q) The median of the above data is | (2) 5 | | (R) The mean deviation about the mean of the above data is | (3) 6 | | (S) The mean deviation about the median of the above data is | (4) 2.7 | | | (5) 2.4 |

$\text{Given: } x_i = 3,8,11,10,5,4;\quad f_i = 5,2,3,2,4,4$ $N = \sum f_i = 5+2+3+2+4+4 = 20$ $\text{To find: mean, median, MD about mean, MD about median}$ $\text{Plan: mean} \to \text{median} \to MD_{\text{mean}} \to MD_{\text{median}}$ $(P)\to?,\ (Q)\to?,\ (R)\to?,\ (S)\to?$ $\sum f_i x_i = 15+16+33+20+20+16 = 120$ $\bar x = \dfrac{120}{20} = 6 \Rightarrow (P)\to(3)$ $\text{Ascending } x_i:\ 3,\ 4,\ 5,\ 8,\ 10,\ 11$ $\text{cumulative } f:\ 5,\ 9,\ 13,\ 15,\ 17,\ 20$ $N/2 = 10 \Rightarrow 10^{\text{th}},\ 11^{\text{th}} \text{ values}$ $\text{Median} = \dfrac{5+5}{2} = 5 \Rightarrow (Q)\to(2)$ $|x_i-\bar x| = |x_i-6|:\quad 3,\ 2,\ 5,\ 4,\ 1,\ 2$ $f_i|x_i-\bar x|:\quad 15,\ 4,\ 15,\ 8,\ 4,\ 8$ $\sum f_i|x_i-\bar x| = 54$ $MD_{\bar x} = \dfrac{54}{20} = 2.7 \Rightarrow (R)\to(4)$ $|x_i-5|:\quad 2,\ 3,\ 6,\ 5,\ 0,\ 1$ $f_i|x_i-5|:\quad 10,\ 6,\ 18,\ 10,\ 0,\ 4$ $\sum f_i|x_i-5| = 48$ $MD_{5} = \dfrac{48}{20} = 2.4 \Rightarrow (S)\to(5)$ $(P)\to(3),\quad (Q)\to(2),\quad (R)\to(4),\quad (S)\to(5)$ $\boxed{\text{Option }(1)}$