Identify the relative locations of the mean and median of a distribution from a density curve.
Skewness affects mean by bringing it closer to the skew. Median is also dragged by skew but not as much. If the graph is symmetric, mean = median.
In a symmetrical density curve, the mean and median are located at the same point since the curve is evenly distributed on each side of its mid-point. This means that the mean and median have the same value.
However, in skewed distributions, the mean and median are not located at the same point. In a positively skewed distribution, the long tail of the curve is on the right-hand side, and the mean is greater than the median. This happens because the relatively few very large scores in the tail pull up the mean.
In a negatively skewed distribution, the long tail of the curve is on the left-hand side, and the median is greater than the mean. This is because the relatively few very small scores in the tail pull down the mean.
Therefore, the relative location of the mean and median in a distribution is dependent on the shape of the curve.
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