Let's analyze and answer the questions based on the data provided in the image:

The list of amounts donated by 9 taxpayers is: $91, 58, 86, 34, 70, 19, 22, 44, 13$

(a) Median:

To find the median, we need to first order the dataLet's analyze and answer the questions based on the data provided in the image:

The list of amounts donated by 9 taxpayers is: $91, 58, 86, 34, 70, 19, 22, 44, 13$

(a) Median:

To find the median, we need to first order the $13, 19, 22, 34, 44, 58, 70, 86, 91$

Since there are 9 numbers, the median is the middle value, which is the 5th number: $\text{Median} = 44$

(b) Mean:

The mean is calculated by summing all the values and dividing by the number of data points.

$\text{Sum} = 13 + 19 + 22 + 34 + 44 + 58 + 70 + 86 + 91 = 437$ $\text{Mean} = \frac{437}{9} \approx 48.6$

(c) Modes:

A mode is the number that appears most frequently in the dataset. Checking the list: $13, 19, 22, 34, 44, 58, 70, 86, 91$

Each number appears exactly once, so there is no mode. The answer is zero modes.

Summary of Answers:

• (a) Median: 44
• (b) Mean: 48.6
• (c) Mode: Zero modes

Do you want more details or have any questions?

Here are five relative questions to deepen understanding:

1. How would the mean change if one more large donation was added?
2. Can a dataset have more than two modes, and what would that look like?
3. What happens to the median if the dataset has an even number of values?
4. How would the range of this dataset be calculated?
5. Is it possible for the mean to be less than the median in a different dataset?

Tip: The mean is sensitive to extreme values (outliers), while the median gives a better sense of the center for skewed distributions.