Q. How are measures of central tendency affected by the shape of the data?

Answer

Common measures of central tendency are the mean, median, and mode. The mode of the data is affected by the number of peaks in the distribution. Multiple peaks in the data result in multiple modes. While the number and location of the peaks have some impact on the mean and median, these estimators are also affected by whether or not the data is skewed.

Skew refers to whether or not the data is symmetrical. If the data is right-skewed (positive skew) it has a tail on the right side, and if the data is left-skewed (negative skew) it has a tail on the left side. If the data is not left- or right-skewed, it is symmetrical.

If the data is relatively symmetrical, the mean and median will produce similar estimates of the center. However, the graphs below show that when the distribution is skewed, the mean is pulled further in the direction of the tail than the median. For this reason, the median is often a more useful estimator of center when the distribution is heavily skewed or there are extreme outliers in the data.

three graphs of positive skew, symmetry, and negative skew. In all three graphs, the mode is at the highest point of the distribution. In the graph where a right (positive) skew is present, the mean is slightly further to the right whereas the median is closer to the peak and is in the center of the distribution. In the graph of the symmetrical distribution, the mode, median, and mean all share the same estimate in the highest and most centered point in the distribution. In the last graph where a negative (left) skew is present, the mean is closer to the left side of the distribution, and the median is between the mean on the mode at the center of the distribution.

  • Last Updated Mar 11, 2021
  • Views 2
  • Answered By Lydia Carter

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