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Let's calculate the population standard deviation for the given data set:

The data points are:
\[ 55, 94, 57, 110, 134, 147, 151, 128 \]

### Step-by-Step Calculation:
1. **Find the mean** (\(\mu\)):
   \[
   \mu = \frac{\sum x_i}{N}
   \]
   Where \(N\) is the number of data points and \(x_i\) represents each data point.

2. **Calculate the squared differences from the mean** (\( (x_i - \mu)^2 \)).

3. **Find the variance** (\(\sigma^2\)):
   \[
   \sigma^2 = \frac{\sum (x_i - \mu)^2}{N}
   \]

4. **Take the square root of the variance to get the standard deviation** (\(\sigma\)).

Let me calculate this for you.The population standard deviation for the given data set is approximately **35.42**, rounded to the nearest hundredth.

Would you like more details on any step of the calculation? 

Here are some related questions to explore:
1. What is the difference between population and sample standard deviation?
2. How is variance related to standard deviation?
3. What is the significance of standard deviation in statistics?
4. How would the calculation change if we added more data points?
5. Can you explain the meaning of dispersion in a data set?

**Tip:** Population standard deviation divides by the total number of data points, while sample standard deviation divides by \( N-1 \).

For the following set of data, find the population standard deviation, to the nearest hundredth: 55, 94, 57, 110, 134, 147, 151, 128.

Calculate the population standard deviation for the data set: 55, 94, 57, 110, 134, 147, 151, 128. Learn how to find the mean, variance, and standard deviation step-by-step, rounded to the nearest hundredth.

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