by hand, find the population variance and standard deviation or the sample variance and standard deviation as indicated. Sample: 6, 52, 13, 49, 35, 25, 31, 29, 31, 29

Let's go through the process of calculating the sample variance and standard deviation by hand for the given sample: 

\[ 6, 52, 13, 49, 35, 25, 31, 29, 31, 29 \]

### Step 1: Find the Sample Mean
The first step is to calculate the mean of the sample. The formula for the sample mean (\(\bar{x}\)) is:

\[
\bar{x} = \frac{\sum x_i}{n}
\]

where \(x_i\) are the sample values and \(n\) is the sample size.

Here, \(n = 10\), and the sum of the sample values is:

\[
\sum x_i = 6 + 52 + 13 + 49 + 35 + 25 + 31 + 29 + 31 + 29 = 300
\]

Now, calculate the sample mean:

\[
\bar{x} = \frac{300}{10} = 30
\]

### Step 2: Calculate Each Deviation from the Mean
Next, subtract the sample mean from each data point to find the deviations:

\[
x_1 - \bar{x} = 6 - 30 = -24
\]
\[
x_2 - \bar{x} = 52 - 30 = 22
\]
\[
x_3 - \bar{x} = 13 - 30 = -17
\]
\[
x_4 - \bar{x} = 49 - 30 = 19
\]
\[
x_5 - \bar{x} = 35 - 30 = 5
\]
\[
x_6 - \bar{x} = 25 - 

By hand, find the population variance and standard deviation or the sample variance and standard deviation as indicated. Sample: 6, 52, 13, 49, 35, 25, 31, 29, 31, 29

Learn how to calculate the sample variance and standard deviation by hand for the data set: 6, 52, 13, 49, 35, 25, 31, 29, 31, 29. This detailed guide covers the steps involved, including finding the sample mean, variance, and standard deviation, suitable for high school students.

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