It looks like you need to calculate the mean, median, mode, range, and standard deviation for the given population of numbers:
$5, 9, 23, 20, 20, 11, 20, 20$

Let's go step by step and correct or verify your answers:

1. Mean (Average): $\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}} = \frac{5 + 9 + 23 + 20 + 20 + 11 + 20 + 20}{8}$ Let me calculate that for you.

2. Median:

   • First, order the numbers:
     $5, 9, 11, 20, 20, 20, 20, 23$
   • Since there are 8 numbers, the median is the average of the 4th and 5th values: $\text{Median} = \frac{20 + 20}{2} = 20$
   • Your median of 20 is correct.

3. Mode:

   • The mode is the number that appears most frequently.
   • In this case, 20 appears 4 times, so the mode is 20.
   • Your mode of 20 is also correct.

4. Range:

   • The range is the difference between the largest and smallest values: $\text{Range} = 23 - 5 = 18$
   • Your range of 18 is correct.

5. Standard Deviation: I'll calculate the standard deviation using the formula for population standard deviation: $\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}$ where $\mu$ is the mean and $N$ is the number of values.

Let me complete these calculations.Here are the correct calculations for the given set of numbers:

1. Mean: 16.00
2. Median: 20
3. Mode: 20
4. Range: 18
5. Standard Deviation: 6.20 (rounded to two decimals)

Your entries for the median, mode, and range are correct, but the mean should be 16.00, and the standard deviation should be 6.20.

Would you like more details on any of these calculations or further clarification?

Here are some related questions to think about:

1. How does the presence of outliers affect the mean and standard deviation?
2. Why does the standard deviation measure variability in a dataset?
3. What would happen to the median if one of the values changed drastically?
4. How do the mode and median help in understanding the shape of a dataset?
5. What is the difference between population standard deviation and sample standard deviation?

Tip: When calculating standard deviation, remember that small datasets are sensitive to changes in values, so always double-check your inputs!