Soalan 5:
Diberi nombor 2, 4, 6, 6, 8 dan 12.
(a) Kenal pasti min, median dan mod bagi set data tersebut.
(b) Hitung min, median dan mod yang baharu jika setiap nombor itu
(i) ditambah 2. (ii) didarab 2.
(iii) ditolak 2. (iv) dibahagi 2.
Penyelesaian:
(a)
$$ \begin{aligned} \operatorname{Min} & =\frac{2+4+6+6+8+12}{6} \\ & =\frac{38}{6} \\ & =6.3 \end{aligned} $$
2, 4, 6, 6, 8, 12.
$$ \begin{aligned} \text { Median } & =\frac{6+6}{2} \\ & =6 \end{aligned} $$
Mod = 6
(b)(i)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal ditambah } 2=4,6,8,8,10,14\\ &\begin{aligned} \operatorname{Min} & =\frac{4+6+8+8+10+14}{6} \\ & =\frac{50}{6} \\ & =8.3 \end{aligned} \end{aligned} $$
4, 6, 8, 8, 10, 14.
$$ \begin{aligned} \text { Median } & =\frac{8+8}{2} \\ & =8 \end{aligned} $$
Mod = 8
(b)(ii)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal didarab } 2=4,8,12,12,16,24\\ &\begin{aligned} \operatorname{Min} & =\frac{4+8+12+12+16+24}{6} \\ & =\frac{76}{6} \\ & =12.7 \end{aligned} \end{aligned} $$
4, 8, 12, 12, 16, 24.
$$ \begin{aligned} \text { Median } & =\frac{12+12}{2} \\ & =12 \end{aligned} $$
Mod = 12
(b)(iii)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal ditolak } 2=0,2,4,4,6,10\\ &\begin{aligned} \operatorname{Min} & =\frac{0+2+4+4+6+10}{6} \\ & =\frac{26}{6} \\ & =4.3 \end{aligned} \end{aligned} $$
0, 2, 4, 4, 6, 10.
$$ \begin{aligned} \text { Median } & =\frac{4+4}{2} \\ & =4 \end{aligned} $$
Mod = 4
(b)(iv)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal dibahagi } 2=1,2,3,3,4,6\\ &\begin{aligned} \operatorname{Min} & =\frac{1+2+3+3+4+6}{6} \\ & =\frac{19}{6} \\ & =3.2 \end{aligned} \end{aligned} $$
1, 2, 3, 3, 4, 6.
$$ \begin{aligned} \text { Median } & =\frac{3+3}{2} \\ & =3 \end{aligned} $$
Mod = 3
Diberi nombor 2, 4, 6, 6, 8 dan 12.
(a) Kenal pasti min, median dan mod bagi set data tersebut.
(b) Hitung min, median dan mod yang baharu jika setiap nombor itu
(i) ditambah 2. (ii) didarab 2.
(iii) ditolak 2. (iv) dibahagi 2.
Penyelesaian:
(a)
$$ \begin{aligned} \operatorname{Min} & =\frac{2+4+6+6+8+12}{6} \\ & =\frac{38}{6} \\ & =6.3 \end{aligned} $$
2, 4, 6, 6, 8, 12.
$$ \begin{aligned} \text { Median } & =\frac{6+6}{2} \\ & =6 \end{aligned} $$
Mod = 6
(b)(i)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal ditambah } 2=4,6,8,8,10,14\\ &\begin{aligned} \operatorname{Min} & =\frac{4+6+8+8+10+14}{6} \\ & =\frac{50}{6} \\ & =8.3 \end{aligned} \end{aligned} $$
4, 6, 8, 8, 10, 14.
$$ \begin{aligned} \text { Median } & =\frac{8+8}{2} \\ & =8 \end{aligned} $$
Mod = 8
(b)(ii)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal didarab } 2=4,8,12,12,16,24\\ &\begin{aligned} \operatorname{Min} & =\frac{4+8+12+12+16+24}{6} \\ & =\frac{76}{6} \\ & =12.7 \end{aligned} \end{aligned} $$
4, 8, 12, 12, 16, 24.
$$ \begin{aligned} \text { Median } & =\frac{12+12}{2} \\ & =12 \end{aligned} $$
Mod = 12
(b)(iii)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal ditolak } 2=0,2,4,4,6,10\\ &\begin{aligned} \operatorname{Min} & =\frac{0+2+4+4+6+10}{6} \\ & =\frac{26}{6} \\ & =4.3 \end{aligned} \end{aligned} $$
0, 2, 4, 4, 6, 10.
$$ \begin{aligned} \text { Median } & =\frac{4+4}{2} \\ & =4 \end{aligned} $$
Mod = 4
(b)(iv)
$$ \begin{aligned} &\text { Data baharu apabila nilai asal dibahagi } 2=1,2,3,3,4,6\\ &\begin{aligned} \operatorname{Min} & =\frac{1+2+3+3+4+6}{6} \\ & =\frac{19}{6} \\ & =3.2 \end{aligned} \end{aligned} $$
1, 2, 3, 3, 4, 6.
$$ \begin{aligned} \text { Median } & =\frac{3+3}{2} \\ & =3 \end{aligned} $$
Mod = 3
Soalan 6:
Diberi min bagi empat nombor ialah 14. Jika dua nombor ditambah dalam set data nombor tersebut, iaitu x dan x + 2, min baharunya ialah 15. Hitung nilai x.
Penyelesaian:
$$ \begin{aligned} \text { Jumlah empat nombor } & =4 \times 14 \\ & =56 \end{aligned} $$
$$ \begin{aligned} \text { Min baharu } & =\frac{56+x+x+2}{6} \\ 15 & =\frac{58+2 x}{6} \\ 15 \times 6 & =58+2 x \\ 90 & =58+2 x \\ -2 x & =58-90 \\ -2 x & =-32 \\ 2 x & =32 \\ x & =\frac{32}{2} \\ & =16 \end{aligned} $$
Diberi min bagi empat nombor ialah 14. Jika dua nombor ditambah dalam set data nombor tersebut, iaitu x dan x + 2, min baharunya ialah 15. Hitung nilai x.
Penyelesaian:
$$ \begin{aligned} \text { Jumlah empat nombor } & =4 \times 14 \\ & =56 \end{aligned} $$
$$ \begin{aligned} \text { Min baharu } & =\frac{56+x+x+2}{6} \\ 15 & =\frac{58+2 x}{6} \\ 15 \times 6 & =58+2 x \\ 90 & =58+2 x \\ -2 x & =58-90 \\ -2 x & =-32 \\ 2 x & =32 \\ x & =\frac{32}{2} \\ & =16 \end{aligned} $$