Whakaoti i te sigma_x^2=(-2-0)^2*4/9+(0*0)^2*3/9+(1*9)^2*2/9

$$\sigma _ { x } ^ { 2 } = ( - 2 - 0 ) ^ { 2 } \times \frac { 4 } { 9 } + ( 0 \times 0 ) ^ { 2 } \times \frac { 3 } { 9 } + ( 1 \times 9 ) ^ { 2 } \times \frac { 2 } { 9 }$$

Whakaoti mō σ_x

$$\sigma _{x}=\frac{\sqrt{178}}{3}\approx 4.447221355$$

$$\sigma _{x}=-\frac{\sqrt{178}}{3}\approx -4.447221355$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 0 i te -2, ka -2.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Tātaihia te -2 mā te pū o 2, kia riro ko 4.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 4 ki te \frac{4}{9}, ka \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 0 ki te 0, ka 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Tātaihia te 0 mā te pū o 2, kia riro ko 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakahekea te hautanga \frac{3}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{1}{3}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 0 ki te \frac{1}{3}, ka 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Tāpirihia te \frac{16}{9} ki te 0, ka \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 1 ki te 9, ka 9.

$$\sigma _{x}^{2}=\frac{16}{9}+9^{2}\times \frac{2}{9}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$\sigma _{x}^{2}=\frac{16}{9}+81\times \frac{2}{9}$$

Whakareatia te 81 ki te \frac{2}{9}, ka 18.

$$\sigma _{x}^{2}=\frac{16}{9}+18$$

Tāpirihia te \frac{16}{9} ki te 18, ka \frac{178}{9}.

$$\sigma _{x}^{2}=\frac{178}{9}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sigma _{x}=\frac{\sqrt{178}}{3} \sigma _{x}=-\frac{\sqrt{178}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 0 i te -2, ka -2.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Tātaihia te -2 mā te pū o 2, kia riro ko 4.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 4 ki te \frac{4}{9}, ka \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 0 ki te 0, ka 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Tātaihia te 0 mā te pū o 2, kia riro ko 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakahekea te hautanga \frac{3}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{1}{3}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 0 ki te \frac{1}{3}, ka 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Tāpirihia te \frac{16}{9} ki te 0, ka \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Whakareatia te 1 ki te 9, ka 9.

$$\sigma _{x}^{2}=\frac{16}{9}+9^{2}\times \frac{2}{9}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$\sigma _{x}^{2}=\frac{16}{9}+81\times \frac{2}{9}$$

Whakareatia te 81 ki te \frac{2}{9}, ka 18.

$$\sigma _{x}^{2}=\frac{16}{9}+18$$

Tāpirihia te \frac{16}{9} ki te 18, ka \frac{178}{9}.

$$\sigma _{x}^{2}=\frac{178}{9}$$

Tangohia te \frac{178}{9} mai i ngā taha e rua.

$$\sigma _{x}^{2}-\frac{178}{9}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{178}{9} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\sigma _{x}=\frac{0±\sqrt{0^{2}-4\left(-\frac{178}{9}\right)}}{2}$$

Pūrua 0.

$$\sigma _{x}=\frac{0±\sqrt{-4\left(-\frac{178}{9}\right)}}{2}$$

Whakareatia -4 ki te -\frac{178}{9}.

$$\sigma _{x}=\frac{0±\sqrt{\frac{712}{9}}}{2}$$

Tuhia te pūtakerua o te \frac{712}{9}.

$$\sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2}$$

Nā, me whakaoti te whārite \sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} ina he tāpiri te ±.

$$\sigma _{x}=\frac{\sqrt{178}}{3}$$

Nā, me whakaoti te whārite \sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} ina he tango te ±.

$$\sigma _{x}=-\frac{\sqrt{178}}{3}$$

Kua oti te whārite te whakatau.

$$\sigma _{x}=\frac{\sqrt{178}}{3} \sigma _{x}=-\frac{\sqrt{178}}{3}$$