To find the sample standard deviation for the biology quiz scores (2, 9, 5, 6, 6), we follow these steps:

Step 1: Find the mean

$\text{Mean} = \frac{2 + 9 + 5 + 6 + 6}{5} = \frac{28}{5} = 5.6$

Step 2: Calculate the squared differences from the mean for each score

• For 2: $(2 - 5.6)^2 = (-3.6)^2 = 12.96$
• For 9: $(9 - 5.6)^2 = (3.4)^2 = 11.56$
• For 5: $(5 - 5.6)^2 = (-0.6)^2 = 0.36$
• For 6: $(6 - 5.6)^2 = (0.4)^2 = 0.16$
• For the second 6: $(6 - 5.6)^2 = (0.4)^2 = 0.16$

Step 3: Find the average of these squared differences

$\text{Variance} = \frac{12.96 + 11.56 + 0.36 + 0.16 + 0.16}{5-1} = \frac{25.2}{4} = 6.3$

Step 4: Take the square root of the variance

$\text{Standard Deviation} = \sqrt{6.3} \approx 2.51$

Thus, the sample standard deviation is approximately 2.51.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How does sample standard deviation differ from population standard deviation?
2. Why do we divide by $n - 1$ in the sample variance formula?
3. What are the properties of standard deviation in data sets?
4. How would the standard deviation change if the data set had a different distribution?
5. How can standard deviation be used to identify outliers in a data set?

Tip: Always remember to subtract 1 from the sample size when calculating sample variance to account for the degrees of freedom.