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The mean and median are central measures of a data set, each giving insights into the typical values you might expect. The mean, often called the average, is calculated by adding up all the values and dividing by the number of values. In formula form, it's given as \( \mu = \frac{1}{n} \sum_{i=1}^{n} x_i \), where \( \mu \) is the mean and \( n \) is the number of data points. In our exercise, the mean is 1000 FTES.

The median, on the other hand, represents the middle value when all data points are ordered from smallest to largest. When the number of data points \( n \) is odd, the median is the middle point. If \( n \) is even, it is the average of the two central numbers. For Lake Tahoe Community College, the median is 1014 FTES, indicating that half the yearly FTES were below this value and half were above.

Both these metrics help describe the central tendency of the data, but the median is often more resilient to outliers. This means if there's an unusually high or low number in the dataset, the median is less affected compared to the mean.

Standard deviation is a statistic that measures the dispersion or variability in a set of data points. It tells us how spread out the numbers are from the mean. A low standard deviation indicates that the data points tend to be close to the mean, whereas a high standard deviation suggests they are spread out over a wider range.

The formula for the standard deviation \( \sigma \) is given as\[ \sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2} \]where \( \mu \) is the mean and \( x_i \) is each individual data point. In the context of Lake Tahoe Community College, the standard deviation is 474 FTES. This implies that the number of full-time equivalent students varies, on average, by 474 from the mean of 1000 FTES.

Understanding standard deviation helps in interpreting the consistency of the data. Smaller standard deviations indicate more stability in the student numbers year over year, whereas larger standard deviations suggest more fluctuations, possibly due to varying enrollment trends or other factors.

Quartiles are values that split data into four equal parts, each containing a quarter of the data points. They are useful in understanding the spread and central location of the data.

• The first quartile (Q1), also known as the lower quartile, is the median of the first half of the data set. For our dataset, Q1 is 528.5 FTES, indicating that 25% of the years had FTES at or below this value.
• The second quartile (Q2) is the median of the entire dataset, which we already identified as 1014 FTES. It signifies the middle point of the dataset.
• The third quartile (Q3) marks the median of the second half of the data and is 1447.5 FTES for this dataset. This means 75% of the data is less than or equal to this value.

Quartiles are particularly useful for detecting and understanding outliers. Data points that lie far outside the interquartile range (Q3 - Q1) may be considered outliers, providing insight into unusual variations in the dataset.