To calculate the standard deviation for this data:

Step 1: Extract the data

The stem-and-leaf plot represents:

• Stem 0 with leaf 6 = 6
• Stem 1 with leaves 1, 6 = 11, 16
• Stem 2 with leaves 1, 6 = 21, 26

The data set is:
$6, 11, 16, 21, 26$

Step 2: Calculate the mean

$\text{Mean} = \frac{\text{Sum of data}}{\text{Number of data points}} = \frac{6 + 11 + 16 + 21 + 26}{5} = \frac{80}{5} = 16$

Step 3: Calculate the squared differences from the mean

For each data point: $(6 - 16)^2 = (-10)^2 = 100$ $(11 - 16)^2 = (-5)^2 = 25$ $(16 - 16)^2 = 0^2 = 0$ $(21 - 16)^2 = 5^2 = 25$ $(26 - 16)^2 = 10^2 = 100$

Step 4: Find the variance

The variance is the average of these squared differences: $\text{Variance} = \frac{\text{Sum of squared differences}}{\text{Number of data points}} = \frac{100 + 25 + 0 + 25 + 100}{5} = \frac{250}{5} = 50$

Step 5: Find the standard deviation

The standard deviation is the square root of the variance: $\text{Standard Deviation} = \sqrt{50} \approx 7.07$

Final Answer:

$\text{Standard Deviation} = 7.07$

Would you like further clarification or additional examples?

Relative Questions:

1. How is variance related to standard deviation?
2. How do you interpret the standard deviation value in this context?
3. What changes if you calculate a sample standard deviation instead of a population standard deviation?
4. Can you compare this result to a different dataset with a higher mean but similar deviation?
5. How would adding an extreme outlier affect the standard deviation?

Tip: The standard deviation provides insight into the data's spread around the mean—smaller values indicate tighter clustering.