What are the differences between the mean, median, and mode? How are they affected by a normal versus a skewed distribution of data?

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Quizplus · Accepted Answer

The Answer is The mean, median, and mode are all measures of central tendency in a set of data.

The mean is the average of all the values in the data set. It is calculated by adding up all the values and then dividing by the total number of values. The mean is affected by extreme values, as it can be heavily influenced by outliers.

The median is the middle value in a data set when the values are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values. The median is not affected by extreme values, making it a more robust measure of central tendency compared to the mean.

The mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode at all. The mode is not affected by extreme values, but it may not be a good representation of the central tendency if the data is spread out.

In a normal distribution of data, the mean, median, and mode are all equal. This is because a normal distribution is symmetric around the mean, so the middle value (median) and the most frequent value (mode) are the same as the average (mean).

In a skewed distribution, the mean, median, and mode can be different. In a positively skewed distribution (tail to the right), the mean is greater than the median, which is greater than the mode. In a negatively skewed distribution (tail to the left), the mean is less than the median, which is less than the mode. This is because the extreme values in the tail of the distribution pull the mean in their direction, while the median and mode are less affected by these extreme values.

What Are the Differences Between the mean, median, and mode