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The mean, also known as the average, is a measure of central tendency that sums all values in a data set and divides by the number of values. To compute the mean for our flight time data set, first, all flight times are summed up. Then, the total sum is divided by the number of flights.

For our given data set, the sum of 257, 260, 260, 266, 267, 270, and 282 is 1862. Since there are 7 flights, the mean flight time is calculated as:
\[ \text{Mean} = \frac{1862}{7} = 266 \]
This means that the average flight time from Las Vegas to Newark on Continental Airlines, in our random sample, is 266 minutes. The mean provides a central value which helps to understand the overall flight duration.

The median is another measure of central tendency that identifies the middle value in a data set arranged in ascending order. When the data set has an odd number of observations, the median is the middle value. If it has an even number of observations, the median is the average of the two central numbers.

For our data set, 257, 260, 260, 266, 267, 270, and 282, which has 7 observations, the median is the 4th value as excited by:
\[ \text{Median} = 266 \]
The median, 266 minutes, represents the middle flight time value, showing that half of the flight times are shorter and half are longer. The median is particularly useful in skewed distributions as it is not easily influenced by extreme values.

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all if no number repeats.

For the ordered flight times 257, 260, 260, 266, 267, 270, and 282, the number 260 appears twice, more often than any other number. Hence, the mode is:
\[ \text{Mode} = 260 \]
The mode helps identify the most common value in the data set. In this context, 260 minutes is the most frequent flight time observed in our sample, providing insight into what time might be expected more commonly.