Solve 1/10left(left(9-8.3right)^2*2+left(8-8.3right)^2*6+left(10-8.3right)^2+left(7-8.3right)^2right)

$$\frac{ 1 }{ 10 } \left( { \left(9-8.3 \right) }^{ 2 } \times 2+ { \left(8-8.3 \right) }^{ 2 } \times 6+ { \left(10-8.3 \right) }^{ 2 } + { \left(7-8.3 \right) }^{ 2 } \right)$$

Evaluate

$$0.61$$

Solution Steps

Subtract 8.3 from 9 to get 0.7.

$$\frac{1}{10}\left(0.7^{2}\times 2+\left(8-8.3\right)^{2}\times 6+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Calculate 0.7 to the power of 2 and get 0.49.

$$\frac{1}{10}\left(0.49\times 2+\left(8-8.3\right)^{2}\times 6+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Multiply 0.49 and 2 to get 0.98.

$$\frac{1}{10}\left(0.98+\left(8-8.3\right)^{2}\times 6+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Subtract 8.3 from 8 to get -0.3.

$$\frac{1}{10}\left(0.98+\left(-0.3\right)^{2}\times 6+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Calculate -0.3 to the power of 2 and get 0.09.

$$\frac{1}{10}\left(0.98+0.09\times 6+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Multiply 0.09 and 6 to get 0.54.

$$\frac{1}{10}\left(0.98+0.54+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Add 0.98 and 0.54 to get 1.52.

$$\frac{1}{10}\left(1.52+\left(10-8.3\right)^{2}+\left(7-8.3\right)^{2}\right)$$

Subtract 8.3 from 10 to get 1.7.

$$\frac{1}{10}\left(1.52+1.7^{2}+\left(7-8.3\right)^{2}\right)$$

Calculate 1.7 to the power of 2 and get 2.89.

$$\frac{1}{10}\left(1.52+2.89+\left(7-8.3\right)^{2}\right)$$

Add 1.52 and 2.89 to get 4.41.

$$\frac{1}{10}\left(4.41+\left(7-8.3\right)^{2}\right)$$

Subtract 8.3 from 7 to get -1.3.

$$\frac{1}{10}\left(4.41+\left(-1.3\right)^{2}\right)$$

Calculate -1.3 to the power of 2 and get 1.69.

$$\frac{1}{10}\left(4.41+1.69\right)$$

Add 4.41 and 1.69 to get 6.1.

$$\frac{1}{10}\times 6.1$$

Multiply \frac{1}{10} and 6.1 to get \frac{61}{100}.

$$\frac{61}{100}$$

Factor

$$\frac{61}{2 ^ {2} \cdot 5 ^ {2}} = 0.61$$