To find the population standard deviation, we follow these steps:

1. Find the Mean (μ):

First, calculate the mean of the data set.

$\mu = \frac{\text{Sum of all data values}}{\text{Number of data values}} = \frac{44 + 46 + 44 + 46 + 45 + 36 + 47}{7} = \frac{308}{7} = 44$

2. Calculate Each Deviation from the Mean and Square It:

Now, subtract the mean from each data value and square the result.

$(44 - 44)^2 = 0^2 = 0$ $(46 - 44)^2 = 2^2 = 4$ $(44 - 44)^2 = 0^2 = 0$ $(46 - 44)^2 = 2^2 = 4$ $(45 - 44)^2 = 1^2 = 1$ $(36 - 44)^2 = (-8)^2 = 64$ $(47 - 44)^2 = 3^2 = 9$

3. Find the Average of These Squared Deviations:

Since this is the population standard deviation, we divide by the total number of data points $N = 7$.

$\text{Variance} = \frac{0 + 4 + 0 + 4 + 1 + 64 + 9}{7} = \frac{82}{7} = 11.714$

4. Take the Square Root of the Variance:

The standard deviation is the square root of the variance.

$\sigma = \sqrt{11.714} \approx 3.423$

So, the population standard deviation is approximately 3.423 (to the nearest thousandth).

Do you want further details or explanations?

Here are 5 questions to expand your understanding:

1. How is the population standard deviation different from sample standard deviation?
2. Can you explain the difference between variance and standard deviation?
3. What does standard deviation indicate about a data set?
4. How would you calculate the sample standard deviation for the same data set?
5. What effect does a single outlier have on the standard deviation?

Tip: Always verify whether you are working with a sample or the entire population when calculating the standard deviation, as the formulas slightly differ.