An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
For test scores with no outliers, the mean is the best measure.
For categorical data like grades, the mode indicates the most frequent grade.
The question (c) is incomplete.
Therefore, the answers are: Mean, Mode, and Incomplete Question.
Explanation
Understand the problem and provided data We are asked to determine the best measure to describe data in three different scenarios. (a) We have a data set of test scores for 10 members of a fraternity: 118, 120, 121, 123, 124, 125, 127, 128, 130, 131. (b) Students receive grades A, B, C, D, or F on a test. (c) We are considering data from the past 9 days.
Analyze scenario (a) (a) To determine whether the mean or median is a better measure for the given test scores, we need to consider if there are any outliers or skewness in the data. The data set is: 118, 120, 121, 123, 124, 125, 127, 128, 130, 131. The data appears to be relatively symmetric and there are no obvious outliers. Therefore, the mean is an appropriate measure to summarize the data.
Analyze scenario (b) (b) We need to determine which measure (mean, median, or mode) tells the grade given most often. Since the data is categorical (grades A, B, C, D, or F), the mode is the appropriate measure. The mode represents the most frequent category.
Analyze scenario (c) (c) The question is incomplete. It does not provide enough information about the data from the past 9 days to determine the best measure to use.
Final Answer (a) The mean should be used to summarize the data. (b) The mode tells the grade given most often. (c) The question is incomplete.
Examples
Understanding which measure to use (mean, median, or mode) is crucial in many real-life situations. For instance, when analyzing income data for a city, the median income is often preferred over the mean income because it is less affected by extremely high incomes of a few individuals. In quality control, the mode can be used to identify the most common defect in a manufacturing process. In weather forecasting, the mean temperature over a period of time helps in understanding climate trends.
