The image you've uploaded contains a set of three questions related to choosing the best measure to describe data. Let's go through each of them:

(a) The 9 members of a fraternity have the following test scores:

118, 119, 120, 122, 123, 124, 128, 130, 131. Which measure should be used to summarize the data?

• Mean, Median, or Mode

To decide the best measure, let's analyze:

• Mean: The mean is the average of all values, which works well for normally distributed data.
• Median: The median is the middle value in an ordered dataset. It's better when the data has outliers or is skewed.
• Mode: The mode represents the most frequent value, which is useful when data has repeated values.

In this case, the data does not have any repeated scores, and it appears relatively symmetrical. Thus, Mean would be the best measure to summarize this data.

(b) In a survey, a soft drink company asks people to name as many brands of soft drinks as they can. Which measure gives the most frequently mentioned brand?

• Mean, Median, or Mode

Here, we are looking for the most frequently mentioned brand. The Mode is the best choice here because it identifies the value that occurs most frequently in a dataset.

(c) In a survey, 9 people gave the following ratings for a local politician (on a scale of 0 to 100):

41, 42, 44, 46, 49, 52, 53, 55, 87. Which measure should be used to summarize the data?

• Mean, Median, or Mode

For this set of ratings, the data seems somewhat skewed due to the higher value (87) compared to the others. The Median would be the most appropriate measure here because it is less affected by extreme values, giving a better central tendency for this skewed data.

Summary of Answers:

• (a) Mean
• (b) Mode
• (c) Median

Would you like any further explanation on any of these? Here are some additional questions you may find helpful:

1. How does the presence of outliers affect the mean and median?
2. When is it better to use the median over the mean?
3. Can you use the mode in data with no repeated values?
4. How would you calculate the mean of a data set?
5. What is the purpose of using measures of central tendency like the mean, median, and mode?

Tip: When dealing with skewed data, the median is often a better measure of central tendency than the mean because it is less influenced by outliers.