Let me extract the mathematical content from the image and calculate the mean, median, mode, and range for the given data. Please hold on.The problem is asking to find the mean, median, mode, and range for the following dataset:
12, 15, 7, 8, 11, 25, 30, 16, 28, 22, 8

Let's calculate step by step:

1. Mean

The formula for the mean is:
$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$
Sum of data points:
$12 + 15 + 7 + 8 + 11 + 25 + 30 + 16 + 28 + 22 + 8 = 182$
Number of data points: $11$
$\text{Mean} = \frac{182}{11} \approx 16.5$

2. Median

The median is the middle value of the dataset when arranged in ascending order.
Sorted data: $7, 8, 8, 11, 12, 15, 16, 22, 25, 28, 30$
Since there are 11 data points (odd), the median is the 6th value:
$\text{Median} = 15$

3. Mode

The mode is the most frequently occurring value.
In the dataset $7, 8, 8, 11, 12, 15, 16, 22, 25, 28, 30$, the number $8$ appears twice.
$\text{Mode} = 8$

4. Range

The range is the difference between the largest and smallest values.
$\text{Range} = \text{Max value} - \text{Min value} = 30 - 7 = 23$

Final Answers:

• Mean: $16.5$
• Median: $15$
• Mode: $8$
• Range: $23$

Would you like further explanation on any of these?

Related Questions:

1. How is the mode affected when there are multiple numbers with the same frequency?
2. What happens to the mean when an extreme value (outlier) is added to the dataset?
3. Can a dataset have no mode? Why or why not?
4. What is the impact on the median if additional data points are added symmetrically?
5. How can the range be misleading when interpreting data?

Tip:

The mean is sensitive to outliers, so always check the data for unusually high or low values before interpreting results.