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The mean is a statistical measure that represents the average of a set of numbers. To calculate it, add up all the numbers and then divide by the count of those numbers. For instance, if you have a data set of 3, 5, and 7, the mean would be \(\frac{3 + 5 + 7}{3} = 5\). The mean is sensitive to outliers, meaning that it can be significantly affected by extremely high or low values in the data set.
In the context of a skewed distribution, especially when skewed to the left, the presence of lower than average outlier values will pull the mean downward. This makes the mean a valuable indicator of such outliers when interpreting data distributions.

The median is the middle value of a data set when it is ordered from least to greatest. It is a robust measure of central tendency because it is not affected by outliers or extreme values like the mean. For example, in a data set ordered as 3, 5, 7, the median is 5. If another data set is 3, 5, 100, the median remains 5 despite the high outlier, showing the median's resistance to skewness.
In a left-skewed distribution, while the mean might be pulled down by outliers on the lower end of the scale, the median stays relatively stable. This stability makes it useful for understanding the central tendency without the influence of extreme values.

Left skewness, also known as negative skewness, occurs when a distribution has a long tail on the left side. This means there are frequent low values compared to high values. In such distributions, the mean is often lower than the median because it is pulled in the direction of the tail by the lower outliers.
Consider a histogram with most of the data points at higher values but a few very low values extending the left tail. This distribution will appear dragged out on the left side, indicating left skewness. Understanding this skewness helps in predicting how the mean will deviate from the median, offering insights into data behavior.

Outliers are data points that differ significantly from other observations. They can be unusually high or low values that can dramatically affect statistical analysis, particularly the mean.
In a left-skewed distribution, outliers occur on the low value side, contributing to the extending tail. This skewness affects the mean more than the median, as these low outliers pull the average down. Outliers can indicate a variety of issues from data collection errors to naturally occurring variability. It's essential to identify them to better understand their effects on the distribution's shape. Knowing the role of outliers in skewness helps in assessing their impact on both mean and median, guiding more accurate interpretations of the data.