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Understanding how to calculate the mean—often referred to as the average—is essential in statistics. The mean is found by adding all the numbers in the dataset together and dividing by the count of the numbers. In mathematical terms, if the dataset is given by the values \(x_1, x_2, \.\.\., x_n\), the formula for the mean \(\mu\) is given by:

\[ \text{Mean (}\mu\text{)} = \frac{x_1 + x_2 + \.\.\. + x_n}{n} \]
where \(n\) is the total number of values. For the example dataset \(2, 5, 6, 7, -1, -1\), adding these up gives us 18, and since there are 6 numbers, our mean is \(\frac{18}{6} = 3\). It's important to remember that the mean is very sensitive to outliers. Extreme values in the dataset can skew the mean, making it less representative of the data as a whole.

The median is the 'middle value' in an ordered list of numbers. To find the median, you need to sort the dataset from smallest to largest. If there's an odd number of data points, the median is the number right in the middle. For an even number of data points, like our example dataset \(2, 5, 6, 7, -1, -1\), you take the average of the middle two numbers after arranging them.

Once sorted: \(-1, -1, 2, 5, 6, 7\), we take the third and fourth numbers: 2 and 5. The median is then calculated as:

\[ \text{Median} = \frac{2^{nd} \text{middle value} + 3^{rd} \text{middle value}}{2} = \frac{2 + 5}{2} = 3.5 \]
The median is less affected by outliers and skewed data than the mean, making it a more accurate reflection for some datasets.

The mode is the value that appears most frequently in a data set. A set may have one mode, more than one mode, or no mode at all. In the provided example dataset \(2, 5, 6, 7, -1, -1\), we can see that the number \(-1\) pops up more than once. Specifically, it appears twice, while all other numbers appear only once.

Therefore, the mode of this dataset is \(-1\). It is the only number that repeats, making it the mode. The mode is particularly useful for categorical data where we wish to know which is the most common category, but it can be applied to numerical data as well. In some cases, where the data points have the same frequency or each point is unique, there may be no mode or several modes to consider.