Previous in Probability and Statistics Next in Probability and Statistics
Question Number 151454 by gsk2684 last updated on 21/Aug/21
$${when}\:{a}\:{die}\:{is}\:{rolled}\:\mathrm{42}\:{times}\:{it}\:{is}\:{so} \\ $$$${happened}\:{that}\:{a}\:{face}\:{having}\:{the}\:{digit}\:{i} \\ $$$${times}\:{occured}\:\mathrm{2}{i}\:{times}.\:{then}\:{find}\:{the} \\ $$$${mean}\:{deviation}\:{from}\:{the}\:{mean}\:{of}\:{this} \\ $$$${discrete}\:{frequency}\:{distribution}. \\ $$$${ans}\:{is}\:\frac{\mathrm{80}}{\mathrm{63}} \\ $$$${sol}\:{pls} \\ $$
Commented by Olaf_Thorendsen last updated on 21/Aug/21
$$\bullet\:{i}\:=\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\} \\ $$$$\bullet\:{x}_{{i}} \:=\:{i} \\ $$$$\bullet\:{n}_{{i}} \:=\:\mathrm{2}{i} \\ $$$$\bullet\:{n}\:=\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{n}_{{i}} =\:\mathrm{42} \\ $$$$\bullet\:{f}_{{i}} \:=\:\frac{{n}_{{i}} }{{n}}\:=\:\frac{\mathrm{2}{i}}{\mathrm{42}}\:=\:\frac{{i}}{\mathrm{21}} \\ $$$$\bullet\:\overset{−} {{x}}\:=\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{f}_{{i}} {x}_{{i}} \:=\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}\frac{{i}^{\mathrm{2}} }{\mathrm{21}}\:=\:\frac{\frac{\mathrm{6}×\mathrm{7}×\mathrm{13}}{\mathrm{6}}}{\mathrm{21}}\:=\:\frac{\mathrm{13}}{\mathrm{3}} \\ $$$$\bullet\:\sigma\:=\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{f}_{{i}} \mid{x}_{{i}} −\overset{−} {{x}}\mid\:=\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}\frac{{i}}{\mathrm{21}}\mid{i}−\frac{\mathrm{13}}{\mathrm{3}}\mid\:=\:\frac{\mathrm{80}}{\mathrm{63}} \\ $$
Commented by gsk2684 last updated on 21/Aug/21
$${dhanyavadhamulu}\left({thanks}\right) \\ $$