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When studying statistics in education, population parameters play a crucial role. These parameters, such as mean, median, and standard deviation, represent characteristics of a whole population. For Lake Tahoe Community College's data, these figures provide insights into the student enrollment trends over nearly three decades. The mean, denoted as \( \mu \), is 1000 FTES, suggesting the average number of full-time students equivalent over the years. The standard deviation, \( \sigma \), is 474 FTES, indicating how much variation there is from the average. These parameters help summarize large datasets into understandable figures, which is valuable for administrators and educators who want to track or predict trends without analyzing each year individually.

The median is the middle value that separates a dataset into two equal halves. For instance, in our student data with 29 years record, the median FTES is 1014. This means that half of the years had less than 1014 FTES, and the other half had more. Understanding the median is important because it provides a measure of central tendency that is not affected by extremely high or low values, known as outliers. When deciding how many years in our sample likely have an FTES of 1014 or more, knowing the median helps in estimating that half of the observations will be above this value when sampling from the population.

Sampling involves selecting a subset of individuals from a population to make inferences about the entire population. In our exercise, we are drawing 11 years from a 29-year span. Sampling allows us to estimate population characteristics without examining the entire dataset. Random sampling, which assumes every year had an equal chance of being chosen, is crucial for achieving unbiased results. By taking 11 years as a sample, we can estimate what proportions of certain characteristics—such as FTES greater than the median—exist in the entire population. This technique is especially useful in statistics education, enabling predictions and analyses with limited resources.

The concept of expected value is fundamental in statistics when predicting outcomes. It refers to the average of all possible values of a random variable weighted by their probabilities. For our problem, we want to predict how many years in a random sample of 11 will have FTES of 1014 or more. Since the median indicates that 50% of the data is above and 50% is below 1014 FTES, we expect half of our sample years to meet or exceed this value. This means, for our sample size of 11, the expected number of years with an FTES of 1014 or greater is approximately 5.5, and we round this to the nearest whole number, getting 6. Understanding expected value helps in making informed predictions and decisions, which is vital in fields like education administration where such data informs strategic planning.