**Find the standard deviation for the following data.**
*Round your answer to 2 decimal places as needed*



66

80

29

57

47

8

37

36

To find the standard deviation, we'll follow these steps:

### Step 1: Calculate the mean (average)
The mean is the sum of all the numbers divided by the total count.

\[
\text{Mean} = \frac{66 + 80 + 29 + 57 + 47 + 8 + 37 + 36}{8} = \frac{360}{8} = 45
\]

### Step 2: Subtract the mean from each data point and square the result
\[
(66 - 45)^2 = 441
\]
\[
(80 - 45)^2 = 1225
\]
\[
(29 - 45)^2 = 256
\]
\[
(57 - 45)^2 = 144
\]
\[
(47 - 45)^2 = 4
\]
\[
(8 - 45)^2 = 1369
\]
\[
(37 - 45)^2 = 64
\]
\[
(36 - 45)^2 = 81
\]

### Step 3: Calculate the variance
The variance is the average of the squared differences. Since this is a sample, we'll divide by \(n - 1 = 8 - 1 = 7\).

\[
\text{Variance} = \frac{441 + 1225 + 256 + 144 + 4 + 1369 + 64 + 81}{7} = \frac{3584}{7} = 512
\]

### Step 4: Calculate the standard deviation
The standard deviation is the square root of the variance.

\[
\text{Standard Deviation} = \sqrt{512} \approx 22.63
\]

So, the standard deviation is approximately **22.63**.

Would you like further details on any step, or have any questions?

Here are 5 relative questions to consider:
1. How is variance related to standard deviation?
2. What is the difference between population and sample standard deviation?
3. Why do we square the differences when calculating variance?
4. How would the standard deviation change if we added more data points?
5. Can standard deviation ever be negative?

**Tip:** Always clarify whether the data represents a sample or the entire population. This affects whether you divide by \(n-1\) (sample) or \(n\) (population) when calculating variance.

Find the standard deviation for the following data

Learn how to find the standard deviation for the data set 66, 80, 29, 57, 47, 8, 37, 36 with a detailed, step-by-step guide. This problem covers essential statistical concepts such as mean, variance, and standard deviation. Suitable for students in Grades 9-12.

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