To compute the population mean and population standard deviation for a given set of random numbers, we will use the formulas:

Population Mean ($\mu$)

$\mu = \frac{\sum x_i}{N}$ Where:

• $\sum x_i$ is the sum of all the values.
• $N$ is the total number of values.

Population Standard Deviation ($\sigma$)

$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}$ Where:

• $\mu$ is the population mean.
• $x_i$ represents each data point.

Let's proceed with the calculations using the given data set of 50 values.The population mean of the given set of random numbers is approximately 56,996.6.

The population standard deviation is approximately 31,236.03.

Would you like further details or have any questions on how these were calculated? Here are some related questions:

1. How would the mean change if a few numbers were much larger than the current ones?
2. What is the difference between a population standard deviation and a sample standard deviation?
3. How can we determine if this distribution is truly uniform?
4. What are other types of distributions, and how do their means and standard deviations behave?
5. How does standard deviation affect the spread of data?

Tip: A higher standard deviation indicates that the data points are spread out over a wider range of values, while a lower standard deviation means the data points are closer to the mean.