Solve frac{left(4-7.5right)^2+left(5-7.5right)^2+left(6-7.5right)^2+left(6-7.5right)^2+{left(6-7.5right)}^{2}+{left(8-7.5right)}^{2}+{left(8-7.5right)}^2+{left(9-7.5right)}^2+{left(10-7.5right)}^2+{left(13-7.5right)}^2}{10}

$$\frac{ { \left(4-7.5 \right) }^{ 2 } + { \left(5-7.5 \right) }^{ 2 } + { \left(6-7.5 \right) }^{ 2 } + { \left(6-7.5 \right) }^{ 2 } + { \left(6-7.5 \right) }^{ 2 } + { \left(8-7.5 \right) }^{ 2 } + { \left(8-7.5 \right) }^{ 2 } + { \left(9-7.5 \right) }^{ 2 } + { \left(10-7.5 \right) }^{ 2 } + { \left(13-7.5 \right) }^{ 2 } }{ 10 }$$

Evaluate

$$6.45$$

Solution Steps

Subtract 7.5 from 4 to get -3.5.

$$\frac{\left(-3.5\right)^{2}+\left(5-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate -3.5 to the power of 2 and get 12.25.

$$\frac{12.25+\left(5-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 5 to get -2.5.

$$\frac{12.25+\left(-2.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate -2.5 to the power of 2 and get 6.25.

$$\frac{12.25+6.25+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 12.25 and 6.25 to get 18.5.

$$\frac{18.5+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 6 to get -1.5.

$$\frac{18.5+\left(-1.5\right)^{2}+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate -1.5 to the power of 2 and get 2.25.

$$\frac{18.5+2.25+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 18.5 and 2.25 to get 20.75.

$$\frac{20.75+\left(6-7.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 6 to get -1.5.

$$\frac{20.75+\left(-1.5\right)^{2}+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate -1.5 to the power of 2 and get 2.25.

$$\frac{20.75+2.25+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 20.75 and 2.25 to get 23.

$$\frac{23+\left(6-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 6 to get -1.5.

$$\frac{23+\left(-1.5\right)^{2}+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate -1.5 to the power of 2 and get 2.25.

$$\frac{23+2.25+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 23 and 2.25 to get 25.25.

$$\frac{25.25+\left(8-7.5\right)^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 8 to get 0.5.

$$\frac{25.25+0.5^{2}+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{25.25+0.25+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 25.25 and 0.25 to get 25.5.

$$\frac{25.5+\left(8-7.5\right)^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 8 to get 0.5.

$$\frac{25.5+0.5^{2}+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{25.5+0.25+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 25.5 and 0.25 to get 25.75.

$$\frac{25.75+\left(9-7.5\right)^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 9 to get 1.5.

$$\frac{25.75+1.5^{2}+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$\frac{25.75+2.25+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Add 25.75 and 2.25 to get 28.

$$\frac{28+\left(10-7.5\right)^{2}+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 10 to get 2.5.

$$\frac{28+2.5^{2}+\left(13-7.5\right)^{2}}{10}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$\frac{28+6.25+\left(13-7.5\right)^{2}}{10}$$

Add 28 and 6.25 to get 34.25.

$$\frac{34.25+\left(13-7.5\right)^{2}}{10}$$

Subtract 7.5 from 13 to get 5.5.

$$\frac{34.25+5.5^{2}}{10}$$

Calculate 5.5 to the power of 2 and get 30.25.

$$\frac{34.25+30.25}{10}$$

Add 34.25 and 30.25 to get 64.5.

$$\frac{64.5}{10}$$

Expand \frac{64.5}{10} by multiplying both numerator and the denominator by 10.

$$\frac{645}{100}$$

Reduce the fraction \frac{645}{100} to lowest terms by extracting and canceling out 5.

$$\frac{129}{20}$$

Factor

$$\frac{3 \cdot 43}{5 \cdot 2 ^ {2}} = 6\frac{9}{20} = 6.45$$