sigma_x^2=(-2-0)^2*4/9+(0*0)^2*3/9+(1*9)^2*2/9 eching

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

σ_x uchun yechish

$$\sigma _{x}=\frac{\sqrt{178}}{3}\approx 4,447221355$$

$$\sigma _{x}=-\frac{\sqrt{178}}{3}\approx -4,447221355$$

Kvadrat ildizini topish bo'yicha qadamlar

-2 olish uchun -2 dan 0 ni ayirish.

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

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

\frac{16}{9} hosil qilish uchun 4 va \frac{4}{9} ni ko'paytirish.

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

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

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

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

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

\frac{3}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

0 hosil qilish uchun 0 va \frac{1}{3} ni ko'paytirish.

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

\frac{16}{9} olish uchun \frac{16}{9} va 0'ni qo'shing.

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

9 hosil qilish uchun 1 va 9 ni ko'paytirish.

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

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

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

18 hosil qilish uchun 81 va \frac{2}{9} ni ko'paytirish.

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

\frac{178}{9} olish uchun \frac{16}{9} va 18'ni qo'shing.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

-2 olish uchun -2 dan 0 ni ayirish.

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

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

\frac{16}{9} hosil qilish uchun 4 va \frac{4}{9} ni ko'paytirish.

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

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

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

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

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

\frac{3}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

0 hosil qilish uchun 0 va \frac{1}{3} ni ko'paytirish.

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

\frac{16}{9} olish uchun \frac{16}{9} va 0'ni qo'shing.

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

9 hosil qilish uchun 1 va 9 ni ko'paytirish.

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

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

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

18 hosil qilish uchun 81 va \frac{2}{9} ni ko'paytirish.

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

\frac{178}{9} olish uchun \frac{16}{9} va 18'ni qo'shing.

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

Ikkala tarafdan \frac{178}{9} ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{178}{9} ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -\frac{178}{9} marotabaga ko'paytirish.

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

\frac{712}{9} ning kvadrat ildizini chiqarish.

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

\sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} tenglamasini yeching, bunda ± musbat.

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

\sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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