Final answer:
The mean is the average of all data points, the median is the middle value in an ordered data set, and the mode is the most frequently occurring value. The mean can be skewed by outliers, the median is less affected by them, and the mode might not reflect skewness. In symmetrical distributions, mean, median, and mode are similar, while in skewed ones, they differ, with the mean showing the most skewness.
Step-by-step explanation:
Differences between mean, median, and mode are fundamental concepts in statistics and central tendency measurement. The mean, also known as the average, is calculated by adding all the values in a data set and dividing by the number of values. It is useful as a measure of central tendency but can be skewed by outliers or extreme values in the data set.
The median is the middle value when a data set is ordered from least to greatest. In a data set with an odd number of values, the median is the middle number; with an even number, it's the average of the two middle numbers. This measure is less affected by outliers and provides a better central tendency estimate in skewed distributions.
The mode refers to the most frequently occurring value(s) in a data set. There can be more than one mode if multiple values have the same highest frequency. In distributions with significant skewness or outliers, the mean will reflect this skewing the most, followed by the median, while the mode might not reflect skewness at all.
In symmetrical distributions, the mean, median, and mode will be equal or very close, indicating no skewness. In a skewed distribution, the mean is pulled toward the tail, and the median will be closer to the mode but not as much as the mean. Understanding these measures helps to interpret and analyze data effectively, allowing for a more accurate representation of a data set's central tendency.