Final answer:
Mean, median, and mode are measures of central tendency in a data set. Mean is the average of all values, median is the middle value when data is sorted, and mode is the most frequent value. Skewness affects the mean the most and helps determine which measure to use.
Step-by-step explanation:
Differences Between Mean, Median, and Mode
Understanding the differences between mean, median, and mode is essential in statistics, as each represents a different aspect of a data set. Mean, often referred to as the average, is calculated by adding all values in the data set and dividing by the number of observations. The formula for mean can be adjusted to approximate values for data that are in ranges.
The median is the middle value in a sorted data set or the average of the two middle numbers if there's an even number of observations. It's particularly useful when a data set contains outliers or extreme values since it is less affected by them compared to the mean.
Mode refers to the most frequently occurring value(s) in a data set. A data set may be unimodal, bimodal, or multimodal depending on if it has one, two, or more modal values respectively. When a distribution is skewed, the mean is most affected by skewness. In left-skewed distributions, the mean is typically less than the median, which is less than the mode, whereas in right-skewed distributions, the mode is often less than the median, which is less than the mean. In a symmetrical distribution, all three measures tend to be the same unless the data set has repeated values, which creates a mode different from the mean and median.
Skewness is crucial as it shows the direction of the spread of data and helps us understand the reliability of the mean as a measure of central tendency. In any analysis involving central tendency, considering the shape of the distribution is essential to choose the most appropriate measure.