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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.

The scores on a sample of biology quizzes are: 2, 9, 5, 6, 6. Find the sample standard deviation of these biology quiz scores. Round to 2 decimal places.

Find the sample standard deviation for the biology quiz scores: 2, 9, 5, 6, 6. This problem involves key statistical concepts, including variance, mean, and the formula for standard deviation. Suitable for students in Grades 9-12.

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