Solve 1/8(left(14.6-14.9right)^2+left(14.7-14.9right)^2+left(15.1-14.9right)^2+left(14.9-14.9right)^2+{left(14.8-14.9right)}^{2}+{left(15.0-14.6right)}^2+{left(15.1-14.9right)}^2+{left(15.2-14.9right)}^2+{left(14.8-14.9right)}^2)

$$\frac{ 1 }{ 8 } ( { \left(14.6-14.9 \right) }^{ 2 } + { \left(14.7-14.9 \right) }^{ 2 } + { \left(15.1-14.9 \right) }^{ 2 } + { \left(14.9-14.9 \right) }^{ 2 } + { \left(14.8-14.9 \right) }^{ 2 } + { \left(15.0-14.6 \right) }^{ 2 } + { \left(15.1-14.9 \right) }^{ 2 } + { \left(15.2-14.9 \right) }^{ 2 } + { \left(14.8-14.9 \right) }^{ 2 } )$$

Evaluate

$$0.06$$

Solution Steps

Subtract 14.9 from 14.6 to get -0.3.

$$\frac{1}{8}\left(\left(-0.3\right)^{2}+\left(14.7-14.9\right)^{2}+\left(15.1-14.9\right)^{2}+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

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

$$\frac{1}{8}\left(0.09+\left(14.7-14.9\right)^{2}+\left(15.1-14.9\right)^{2}+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 14.7 to get -0.2.

$$\frac{1}{8}\left(0.09+\left(-0.2\right)^{2}+\left(15.1-14.9\right)^{2}+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate -0.2 to the power of 2 and get 0.04.

$$\frac{1}{8}\left(0.09+0.04+\left(15.1-14.9\right)^{2}+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Add 0.09 and 0.04 to get 0.13.

$$\frac{1}{8}\left(0.13+\left(15.1-14.9\right)^{2}+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 15.1 to get 0.2.

$$\frac{1}{8}\left(0.13+0.2^{2}+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate 0.2 to the power of 2 and get 0.04.

$$\frac{1}{8}\left(0.13+0.04+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Add 0.13 and 0.04 to get 0.17.

$$\frac{1}{8}\left(0.17+\left(14.9-14.9\right)^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 14.9 to get 0.

$$\frac{1}{8}\left(0.17+0^{2}+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate 0 to the power of 2 and get 0.

$$\frac{1}{8}\left(0.17+0+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Add 0.17 and 0 to get 0.17.

$$\frac{1}{8}\left(0.17+\left(14.8-14.9\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 14.8 to get -0.1.

$$\frac{1}{8}\left(0.17+\left(-0.1\right)^{2}+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate -0.1 to the power of 2 and get 0.01.

$$\frac{1}{8}\left(0.17+0.01+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Add 0.17 and 0.01 to get 0.18.

$$\frac{1}{8}\left(0.18+\left(15-14.6\right)^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.6 from 15 to get 0.4.

$$\frac{1}{8}\left(0.18+0.4^{2}+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate 0.4 to the power of 2 and get 0.16.

$$\frac{1}{8}\left(0.18+0.16+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Add 0.18 and 0.16 to get 0.34.

$$\frac{1}{8}\left(0.34+\left(15.1-14.9\right)^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 15.1 to get 0.2.

$$\frac{1}{8}\left(0.34+0.2^{2}+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate 0.2 to the power of 2 and get 0.04.

$$\frac{1}{8}\left(0.34+0.04+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Add 0.34 and 0.04 to get 0.38.

$$\frac{1}{8}\left(0.38+\left(15.2-14.9\right)^{2}+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 15.2 to get 0.3.

$$\frac{1}{8}\left(0.38+0.3^{2}+\left(14.8-14.9\right)^{2}\right)$$

Calculate 0.3 to the power of 2 and get 0.09.

$$\frac{1}{8}\left(0.38+0.09+\left(14.8-14.9\right)^{2}\right)$$

Add 0.38 and 0.09 to get 0.47.

$$\frac{1}{8}\left(0.47+\left(14.8-14.9\right)^{2}\right)$$

Subtract 14.9 from 14.8 to get -0.1.

$$\frac{1}{8}\left(0.47+\left(-0.1\right)^{2}\right)$$

Calculate -0.1 to the power of 2 and get 0.01.

$$\frac{1}{8}\left(0.47+0.01\right)$$

Add 0.47 and 0.01 to get 0.48.

$$\frac{1}{8}\times 0.48$$

Multiply \frac{1}{8} and 0.48 to get \frac{3}{50}.

$$\frac{3}{50}$$

Factor

$$\frac{3}{2 \cdot 5 ^ {2}} = 0.06$$