Find the standard deviation for the group of data items. $$ 5,6,7,8,9 $$ The standard deviation is (Round to two decimal places as needed.)

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Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{\frac{1}{5}\left(\left(5-7\right)^{2}+\left(6-7\right)^{2}+\left(7-7\right)^{2}+\left(8-7\right)^{2}+\left(9-7\right)^{2}\right)}$$
- step1: Subtract the terms:
  $$\sqrt{\frac{1}{5}\left(\left(5-7\right)^{2}+\left(6-7\right)^{2}+0^{2}+\left(8-7\right)^{2}+\left(9-7\right)^{2}\right)}$$
- step2: Subtract the numbers:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+\left(6-7\right)^{2}+0^{2}+\left(8-7\right)^{2}+\left(9-7\right)^{2}\right)}$$
- step3: Subtract the numbers:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+\left(-1\right)^{2}+0^{2}+\left(8-7\right)^{2}+\left(9-7\right)^{2}\right)}$$
- step4: Subtract the numbers:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+\left(-1\right)^{2}+0^{2}+1^{2}+\left(9-7\right)^{2}\right)}$$
- step5: Subtract the numbers:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+\left(-1\right)^{2}+0^{2}+1^{2}+2^{2}\right)}$$
- step6: Evaluate the power:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+1+0^{2}+1^{2}+2^{2}\right)}$$
- step7: Calculate:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+1+0+1^{2}+2^{2}\right)}$$
- step8: Evaluate the power:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+1+0+1+2^{2}\right)}$$
- step9: Remove 0:
  $$\sqrt{\frac{1}{5}\left(\left(-2\right)^{2}+1+1+2^{2}\right)}$$
- step10: Add the numbers:
  $$\sqrt{\frac{1}{5}\times 10}$$
- step11: Multiply the numbers:
  $$\sqrt{2}$$
Round the number $$ 1.414214 $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$1.414214$$ to $$2$$ decimal places using standard rounding method:
  $$1.414214$$
- step1: Round $$1.414214$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$1.41$$
To find the standard deviation of the data set $$ 5, 6, 7, 8, 9 $$, we follow these steps:

1. **Calculate the mean ($$ \mu $$)**:
   $$
   \mu = \frac{5 + 6 + 7 + 8 + 9}{5} = \frac{35}{5} = 7
   $$

2. **Calculate the squared differences from the mean**:
   - For $$ 5 $$: $$ (5 - 7)^2 = (-2)^2 = 4 $$
   - For $$ 6 $$: $$ (6 - 7)^2 = (-1)^2 = 1 $$
   - For $$ 7 $$: $$ (7 - 7)^2 = (0)^2 = 0 $$
   - For $$ 8 $$: $$ (8 - 7)^2 = (1)^2 = 1 $$
   - For $$ 9 $$: $$ (9 - 7)^2 = (2)^2 = 4 $$

3. **Sum the squared differences**:
   $$
   4 + 1 + 0 + 1 + 4 = 10
   $$

4. **Calculate the variance ($$ \sigma^2 $$)**:
   $$
   \sigma^2 = \frac{10}{5} = 2
   $$

5. **Calculate the standard deviation ($$ \sigma $$)**:
   $$
   \sigma = \sqrt{2} \approx 1.414214
   $$

6. **Round to two decimal places**:
   $$
   \sigma \approx 1.41
   $$

Thus, the standard deviation of the data set is **1.41**.
The standard deviation is **1.41**.

Find the standard deviation for the group of data items. \( 5,6,7,8,9 \) The standard deviation is (Round to two decimal places as needed.)

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