Final answer:
The mean is the arithmetic average, the median is the midpoint value of an ordered data set, and the mode is the most frequently occurring number in the set.
Step-by-step explanation:
The mean, median, and mode are measures of central tendency that help us describe the center of a data set. They provide different ways of finding the average or most common values within a given set of numbers.
Mean
The mean is the arithmetic average of a set of numbers. It is calculated by adding up all the numbers and then dividing by the count of numbers. For example, if the set of numbers is 7, 7, 8, and 9, the mean is (7 + 7 + 8 + 9) / 4, which equals 7.75. The mean is sensitive to outliers and can be skewed by them.
Median
The median is the middle value when a set of numbers is ordered from smallest to largest. If there is an even number of observations, the median is the mean of the two middle numbers. For instance, with the ordered set 7, 7, 8, 9, the median would be (7 + 8) / 2, which equals 7.5. The median is a better measure of center when there are outliers present, as it is not affected by them as much as the mean.
Mode
The mode is the number that appears most frequently in a data set. In the example set 7, 7, 8, 9, the mode is 7 since it appears twice. It's possible for a set to have more than one mode (bimodal) or no mode at all if no number repeats.
In summary, the mean offers a mathematical average, the median provides a midpoint that divides the data into two equal parts, and the mode indicates the most frequently occurring values.