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Question Number 151602 by DELETED last updated on 22/Aug/21
Answered by DELETED last updated on 22/Aug/21
1.g). Letak persentil ke−65 P_i =((i(N+1))/(100)) →P_(65) =((65(25+1))/(100)) =((65×26)/(100))=16,9 Nilai persentil ke 65=x_(16) +0,9(x_(17) −x_(16) ) =19+0,9=19,9
$$\left.\mathrm{1}.\mathrm{g}\right).\:\mathrm{Letak}\:\mathrm{persentil}\:\mathrm{ke}−\mathrm{65} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{P}_{\mathrm{i}} =\frac{\mathrm{i}\left(\mathrm{N}+\mathrm{1}\right)}{\mathrm{100}}\:\rightarrow\mathrm{P}_{\mathrm{65}} \:=\frac{\mathrm{65}\left(\mathrm{25}+\mathrm{1}\right)}{\mathrm{100}} \\ $$$$\:\:\:\:=\frac{\mathrm{65}×\mathrm{26}}{\mathrm{100}}=\mathrm{16},\mathrm{9} \\ $$$$\:\:\:\:\mathrm{Nilai}\:\mathrm{persentil}\:\mathrm{ke}\:\mathrm{65}=\mathrm{x}_{\mathrm{16}} +\mathrm{0},\mathrm{9}\left(\mathrm{x}_{\mathrm{17}} −\mathrm{x}_{\mathrm{16}} \right) \\ $$$$\:\:\:=\mathrm{19}+\mathrm{0},\mathrm{9}=\mathrm{19},\mathrm{9} \\ $$
Answered by DELETED last updated on 22/Aug/21
1.a). x^− = ((Σx_i )/N) =((91+93+85+86+95)/(25)) =((184+171+95)/(25))=((355+95)/(25))=((450)/(25))=18 b). median =nilai data yg ke−13 diurutkan dari yg terkecil 12,13,13,14,14,15,16,16,16, 17,17,18,18,18,... jadi nilai median=18
$$\left.\mathrm{1}.\mathrm{a}\right).\:\:\overset{−} {\mathrm{x}}\:=\:\frac{\Sigma\mathrm{x}_{\mathrm{i}} }{\mathrm{N}}\:=\frac{\mathrm{91}+\mathrm{93}+\mathrm{85}+\mathrm{86}+\mathrm{95}}{\mathrm{25}} \\ $$$$\:\:\:\:\:\:\:\:=\frac{\mathrm{184}+\mathrm{171}+\mathrm{95}}{\mathrm{25}}=\frac{\mathrm{355}+\mathrm{95}}{\mathrm{25}}=\frac{\mathrm{450}}{\mathrm{25}}=\mathrm{18} \\ $$$$\left.\:\:\:\mathrm{b}\right).\:\mathrm{median}\:=\mathrm{nilai}\:\mathrm{data}\:\mathrm{yg}\:\mathrm{ke}−\mathrm{13} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{diurutkan}\:\mathrm{dari}\:\mathrm{yg}\:\mathrm{terkecil} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{12},\mathrm{13},\mathrm{13},\mathrm{14},\mathrm{14},\mathrm{15},\mathrm{16},\mathrm{16},\mathrm{16}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{17},\mathrm{17},\mathrm{18},\mathrm{18},\mathrm{18},… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{jadi}\:\mathrm{nilai}\:\mathrm{median}=\mathrm{18} \\ $$
Answered by DELETED last updated on 22/Aug/21
1.c). 12,13,13,14,14,15,16,16,16, 17,17,18,18,18,19,19,20, 20,20,20,22,22,23,23,25 nilai modus adalah nilai yg paling banyak yaitu=20// 1.d). Kuartil 1= ((x_6 +x_7 )/2) =((15+16)/2)=15,5// 1.e). kuartil 3=((x_(19) +x_(20) )/2)=((20+20)/2)=20//
$$\left.\mathrm{1}.\mathrm{c}\right).\:\:\:\mathrm{12},\mathrm{13},\mathrm{13},\mathrm{14},\mathrm{14},\mathrm{15},\mathrm{16},\mathrm{16},\mathrm{16}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17},\mathrm{17},\mathrm{18},\mathrm{18},\mathrm{18},\mathrm{19},\mathrm{19},\mathrm{20}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{20},\mathrm{20},\mathrm{20},\mathrm{22},\mathrm{22},\mathrm{23},\mathrm{23},\mathrm{25} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{nilai}\:\mathrm{modus}\:\mathrm{adalah}\:\mathrm{nilai} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{yg}\:\mathrm{paling}\:\mathrm{banyak}\:\mathrm{yaitu}=\mathrm{20}// \\ $$$$\left.\mathrm{1}.\mathrm{d}\right).\:\:\:\:\mathrm{Kuartil}\:\mathrm{1}=\:\frac{\mathrm{x}_{\mathrm{6}} +\mathrm{x}_{\mathrm{7}} }{\mathrm{2}}\:=\frac{\mathrm{15}+\mathrm{16}}{\mathrm{2}}=\mathrm{15},\mathrm{5}// \\ $$$$\left.\mathrm{1}.\mathrm{e}\right).\:\mathrm{kuartil}\:\mathrm{3}=\frac{\mathrm{x}_{\mathrm{19}} +\mathrm{x}_{\mathrm{20}} }{\mathrm{2}}=\frac{\mathrm{20}+\mathrm{20}}{\mathrm{2}}=\mathrm{20}// \\ $$
Answered by DELETED last updated on 22/Aug/21
langkah cari kuartil pakai rumus •Letak kuartil ke−i=((i(N+1))/(10)) letak Q_1 =((1(25+1))/4) =((26)/4)=6,5 nilai Q_1 =x_6 +0,5(x_7 −x_6 ) =15+0,5(16−15)=15+0,5=15,5
$$\mathrm{langkah}\:\mathrm{cari}\:\mathrm{kuartil}\:\mathrm{pakai}\:\mathrm{rumus} \\ $$$$\bullet\mathrm{Letak}\:\mathrm{kuartil}\:\mathrm{ke}−\mathrm{i}=\frac{\mathrm{i}\left(\mathrm{N}+\mathrm{1}\right)}{\mathrm{10}} \\ $$$$\:\:\:\mathrm{letak}\:\mathrm{Q}_{\mathrm{1}} =\frac{\mathrm{1}\left(\mathrm{25}+\mathrm{1}\right)}{\mathrm{4}}\:=\frac{\mathrm{26}}{\mathrm{4}}=\mathrm{6},\mathrm{5} \\ $$$$\:\:\:\mathrm{nilai}\:\mathrm{Q}_{\mathrm{1}} =\mathrm{x}_{\mathrm{6}} +\mathrm{0},\mathrm{5}\left(\mathrm{x}_{\mathrm{7}} −\mathrm{x}_{\mathrm{6}} \right) \\ $$$$\:\:\:=\mathrm{15}+\mathrm{0},\mathrm{5}\left(\mathrm{16}−\mathrm{15}\right)=\mathrm{15}+\mathrm{0},\mathrm{5}=\mathrm{15},\mathrm{5} \\ $$
Answered by DELETED last updated on 22/Aug/21
Jawab no 2 a). x^− = ((Σx_i .f_i )/(Σf_i )) =((43×4+44×6+45×4+46×8+47×3+48×4)/(4+6+4+8+3+4)) =((172+264+180+368+141+192)/(29)) =((1317)/(29))=45,41//
$$\mathrm{Jawab}\:\mathrm{no}\:\mathrm{2} \\ $$$$\left.\mathrm{a}\right).\:\overset{−} {\mathrm{x}}\:=\:\frac{\Sigma\mathrm{x}_{\mathrm{i}} .\mathrm{f}_{\mathrm{i}} }{\Sigma\mathrm{f}_{\mathrm{i}} } \\ $$$$\:\:\:\:\:\:=\frac{\mathrm{43}×\mathrm{4}+\mathrm{44}×\mathrm{6}+\mathrm{45}×\mathrm{4}+\mathrm{46}×\mathrm{8}+\mathrm{47}×\mathrm{3}+\mathrm{48}×\mathrm{4}}{\mathrm{4}+\mathrm{6}+\mathrm{4}+\mathrm{8}+\mathrm{3}+\mathrm{4}} \\ $$$$=\frac{\mathrm{172}+\mathrm{264}+\mathrm{180}+\mathrm{368}+\mathrm{141}+\mathrm{192}}{\mathrm{29}} \\ $$$$=\frac{\mathrm{1317}}{\mathrm{29}}=\mathrm{45},\mathrm{41}// \\ $$$$ \\ $$
Answered by DELETED last updated on 22/Aug/21
Letak median=((2(N+1))/4) =((2(29+1))/4)=((30)/2)=15 jadi median=x_(15) =45//
$$\mathrm{Letak}\:\mathrm{median}=\frac{\mathrm{2}\left(\mathrm{N}+\mathrm{1}\right)}{\mathrm{4}} \\ $$$$=\frac{\mathrm{2}\left(\mathrm{29}+\mathrm{1}\right)}{\mathrm{4}}=\frac{\mathrm{30}}{\mathrm{2}}=\mathrm{15} \\ $$$$\mathrm{jadi}\:\mathrm{median}=\mathrm{x}_{\mathrm{15}} =\mathrm{45}// \\ $$$$ \\ $$$$ \\ $$

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