Final answer:
These measures help researchers summarize data collected from samples and make generalizations about the entire population. Understanding these concepts is vital for accurate data analysis and inference. The correct option is A.
Step-by-step explanation:
The question pertains to the field of statistics within mathematics, more specifically to the concept of measures of central tendency and the use of samples to estimate population parameters. The various options provided in the question—sample mean, population mean, median, and mode—are different statistical measures used to summarize and describe data sets. Option A refers to the sample mean, which is the arithmetic average of scores obtained from a subset of the population (the sample). Option B reflects the population mean, that is, the average score of the entire population. Option C describes the median, which is the middle value in a data set when it is ordered from least to greatest. Option D is the mode, the most frequently occurring value in the data set.
Understanding these terms is essential in statistics to make inferences about a given population based on a sample. For instance, when researchers collect data from a sample, they calculate these measures of central tendency to get a sense of what a typical score looks like. Moreover, it's important to understand that while the mean is a useful measure for further analysis, it is sensitive to outliers. The median and mode can sometimes be more representative of a typical value in a skewed distribution.
For example, when a sample mean is calculated from a given sample, researchers can use this statistic to estimate the population mean, especially if the sampling is done correctly to ensure the sample is representative of the population. Repeated sampling would show that the sample mean could vary but should approximate the population mean given no bias in sampling. When dealing with small samples, such as the paired data in the anxiety level study, methods involving dependent means would be used to test hypotheses.