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.)

Question

UpStudy AI · Accepted Answer

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.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Statistics Questions