02711 08182 75997 79866 58095 83319 80295 79741 74599 84379
94873 90935 31684 63952 09865 14491 99518 93394 34691 14985
54921 78680 06635 98689 17306 25170 65928 87709 30533 89736
77640 97636 37397 93379 56454 59818 45827 74164 71666 46977
61545 00835 93251 87203 36759 49197 85967 01704 19634 21898 Compute the population mean and standard deviation of the uniform distribution of random numbers.

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.

Compute the population mean and standard deviation of the uniform distribution of random numbers: 02711 08182 75997 79866 58095 83319 80295 79741 74599 84379 94873 90935 31684 63952 09865 14491 99518 93394 34691 14985 54921 78680 06635 98689 17306 25170 65928 87709 30533 89736 77640 97636 37397 93379 56454 59818 45827 74164 71666 46977 61545 00835 93251 87203 36759 49197 85967 01704 19634 21898

Learn how to compute the population mean and standard deviation for a uniform distribution of random numbers, featuring a step-by-step calculation. Understand core statistical concepts with this guide, suitable for high school students in Grades 10-12.

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