Question-40591

Question Number 40591 by mondodotto@gmail.com last updated on 24/Jul/18

Commented by mondodotto@gmail.com last updated on 24/Jul/18

$$\boldsymbol{\mathrm{roman}}\:\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{please}} \\ $$

Answered by MJS last updated on 24/Jul/18

1−3−11−21−43−32−9 sum=120 120:4=30 persons in each quartile 1+3+11+15of21 ⇒ q1∈[60−69] 6of21+24of43 ⇒ median∈[70−79] 19of43+11of32 ⇒ q3∈[80−89] 21of32+9

$$\mathrm{1}−\mathrm{3}−\mathrm{11}−\mathrm{21}−\mathrm{43}−\mathrm{32}−\mathrm{9} \\ $$$$\mathrm{sum}=\mathrm{120} \\ $$$$\mathrm{120}:\mathrm{4}=\mathrm{30}\:\mathrm{persons}\:\mathrm{in}\:\mathrm{each}\:\mathrm{quartile} \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{11}+\mathrm{15of21}\:\Rightarrow\:\mathrm{q1}\in\left[\mathrm{60}−\mathrm{69}\right] \\ $$$$\mathrm{6of21}+\mathrm{24of43}\:\Rightarrow\:\mathrm{median}\in\left[\mathrm{70}−\mathrm{79}\right] \\ $$$$\mathrm{19of43}+\mathrm{11of32}\:\Rightarrow\:\mathrm{q3}\in\left[\mathrm{80}−\mathrm{89}\right] \\ $$$$\mathrm{21of32}+\mathrm{9} \\ $$

Commented by mondodotto@gmail.com last updated on 25/Jul/18

$$\boldsymbol{\mathrm{sir}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{stil}}\:\boldsymbol{\mathrm{dont}}\:\boldsymbol{\mathrm{undstnd}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{way}} \\ $$

Commented by MJS last updated on 25/Jul/18

to find the borders of the quartiles you have to make a sorted set of all the items and cut this set in 4 parts of equal lenght. there′s no other way. example: the ages of 18 family members {6, 9, 10, 22, 24, 25, 28, 38, 41, 45, 46, 48, 49, 67, 69, 74, 75, 86} 1^(st) half {6, 9, 10, 22, 24, 25, 28, 38, 41} 2^(nd) half {45, 46, 48, 49, 67, 69, 74, 75, 86} median=((41+45)/2)=43 1^(st) quarter {6, 9, 10, 22, 24} 2^(nd) quarter {24, 25, 28, 38, 41} q1=24 3^(rd) quarter {45, 46, 48, 49, 67} 4^(th) quarter {67, 69, 74, 75, 86} q3=67 {min, q1, med, q3, max}={6, 24, 43, 67, 86}

$$\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{borders}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quartiles}\:\mathrm{you}\:\mathrm{have} \\ $$$$\mathrm{to}\:\mathrm{make}\:\mathrm{a}\:\mathrm{sorted}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{items}\:\mathrm{and}\:\mathrm{cut} \\ $$$$\mathrm{this}\:\mathrm{set}\:\mathrm{in}\:\mathrm{4}\:\mathrm{parts}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{lenght}.\:\mathrm{there}'\mathrm{s}\:\mathrm{no} \\ $$$$\mathrm{other}\:\mathrm{way}. \\ $$$$\mathrm{example}: \\ $$$$\mathrm{the}\:\mathrm{ages}\:\mathrm{of}\:\mathrm{18}\:\mathrm{family}\:\mathrm{members} \\ $$$$\left\{\mathrm{6},\:\mathrm{9},\:\mathrm{10},\:\mathrm{22},\:\mathrm{24},\:\mathrm{25},\:\mathrm{28},\:\mathrm{38},\:\mathrm{41},\:\mathrm{45},\:\mathrm{46},\:\mathrm{48},\:\mathrm{49},\:\mathrm{67},\:\mathrm{69},\:\mathrm{74},\:\mathrm{75},\:\mathrm{86}\right\} \\ $$$$\mathrm{1}^{\mathrm{st}} \:\mathrm{half} \\ $$$$\left\{\mathrm{6},\:\:\mathrm{9},\:\mathrm{10},\:\mathrm{22},\:\mathrm{24},\:\mathrm{25},\:\mathrm{28},\:\mathrm{38},\:\mathrm{41}\right\} \\ $$$$\mathrm{2}^{\mathrm{nd}} \:\mathrm{half} \\ $$$$\left\{\mathrm{45},\:\mathrm{46},\:\mathrm{48},\:\mathrm{49},\:\mathrm{67},\:\mathrm{69},\:\mathrm{74},\:\mathrm{75},\:\mathrm{86}\right\} \\ $$$${median}=\frac{\mathrm{41}+\mathrm{45}}{\mathrm{2}}=\mathrm{43} \\ $$$$\mathrm{1}^{\mathrm{st}} \:\mathrm{quarter} \\ $$$$\left\{\mathrm{6},\:\:\mathrm{9},\:\mathrm{10},\:\mathrm{22},\:\mathrm{24}\right\} \\ $$$$\mathrm{2}^{\mathrm{nd}} \:\mathrm{quarter} \\ $$$$\left\{\mathrm{24},\:\mathrm{25},\:\mathrm{28},\:\mathrm{38},\:\mathrm{41}\right\} \\ $$$${q}\mathrm{1}=\mathrm{24} \\ $$$$\mathrm{3}^{\mathrm{rd}} \:\mathrm{quarter} \\ $$$$\left\{\mathrm{45},\:\mathrm{46},\:\mathrm{48},\:\mathrm{49},\:\mathrm{67}\right\} \\ $$$$\mathrm{4}^{\mathrm{th}} \:\mathrm{quarter} \\ $$$$\left\{\mathrm{67},\:\mathrm{69},\:\mathrm{74},\:\mathrm{75},\:\mathrm{86}\right\} \\ $$$${q}\mathrm{3}=\mathrm{67} \\ $$$$\left\{{min},\:{q}\mathrm{1},\:{med},\:{q}\mathrm{3},\:{max}\right\}=\left\{\mathrm{6},\:\mathrm{24},\:\mathrm{43},\:\mathrm{67},\:\mathrm{86}\right\} \\ $$

Commented by mondodotto@gmail.com last updated on 25/Jul/18

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$$$ \\ $$

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