Find the sample standard deviation. Round to the nearest tenth.

15    42    53    7    9    12    14    28    47

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Part 1

A.

17.8

B.

29.1

C.

16.6

D.

15.8

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

1. **Calculate the mean** of the data set.
2. **Subtract the mean** from each data point and **square the result**.
3. **Sum** these squared differences.
4. **Divide** by the number of data points minus one (this is the sample variance).
5. **Take the square root** of the variance to get the standard deviation.

Let's go through these steps with your dataTo find the sample standard deviation, we'll follow these steps:

1. **Calculate the mean** of the data set.
2. **Subtract the mean** from each data point and **square the result**.
3. **Sum** these squared differences.
4. **Divide** by the number of data points minus one (this is the sample variance).
5. **Take the square root** of the variance to get the standard deviation.

Let's go through these steps with your 

### Step 1: Calculate the mean
\[
\text{Mean} = \frac{15 + 42 + 53 + 7 + 9 + 12 + 14 + 28 + 47}{9} = \frac{227}{9} \approx 25.2
\]

### Step 2: Subtract the mean and square the result
- \((15 - 25.2)^2 \approx 104.04\)
- \((42 - 25.2)^2 \approx 282.24\)
- \((53 - 25.2)^2 \approx 774.24\)
- \((7 - 25.2)^2 \approx 331.24\)
- \((9 - 25.2)^2 \approx 262.44\)
- \((12 - 25.2)^2 \approx 173.44\)
- \((14 - 25.2)^2 \approx 125.44\)
- \((28 - 25.2)^2 \approx 7.84\)
- \((47 - 25.2)^2 \approx 475.24\)

### Step 3: Sum these squared differences
\[
\text{Sum of squared differences} = 104.04 + 282.24 + 774.24 + 331.24 + 262.44 + 173.44 + 125.44 + 7.84 + 475.24 = 2536.16
\]

### Step 4: Divide by \(n-1\) to find the variance
\[
\text{Variance} = \frac{2536.16}{8} \approx 317.02
\]

### Step 5: Take the square root of the variance to get the standard deviation
\[
\text{Standard Deviation} = \sqrt{317.02} \approx 17.8
\]

So, the correct answer is **A. 17.8**.

Would you like more details or have any questions?

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**Related Questions:**

1. How do you calculate the population standard deviation?
2. What is the difference between sample and population standard deviation?
3. How does the sample size affect the standard deviation?
4. Can standard deviation be negative?
5. What is the significance of standard deviation in data analysis?

**Tip:** Always remember to use \( n-1 \) instead of \( n \) when calculating the sample standard deviation to account for the sample's degrees of freedom.

Find the sample standard deviation. Round to the nearest tenth.

15    42    53    7    9    12    14    28    47

A.
17.8

B.
29.1

C.
16.6

D.
15.8

This guide explains how to calculate the sample standard deviation for the data set {15, 42, 53, 7, 9, 12, 14, 28, 47}, including step-by-step instructions on finding the mean, variance, and standard deviation. Suitable for students in Grades 9-12.

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