Question Video: Comparing Measures of Centrality in Context

Video Transcript

The following table shows the greatest distances thrown by the finalists in the discus competition of the 2016 Rio Olympics for both men and women. The following summary statistics have been calculated. Why is there a greater difference between the mean and the median for women than there is for men?

Our first table gives the greatest distances thrown by the eight men and eight women in the discus final. The gold medal throw for men was 68.37 meters and the eighth place throw was 63.72 meters. The corresponding values for women were 69.21 meters and 63.06 meters. We are also given the mean and median values for the men and women. For the men, the mean was 65.98 meters and the median 65.84 meters. For the women, the mean was 64.98 meters and the median was 64.64 meters.

In order to calculate the mean, we divide the sum of all the values by the number of values. This means that every single value of our dataset is used when calculating the mean. The median, on the other hand, is the middle value when our dataset is in ascending or descending order. If we have an odd number of values, the median will be a single value, whereas if we have an even number of values, it will be between two values. In this question, the median will be halfway between the fourth and fifth value for men and women.

As a result of how we calculate the median, we are only interested in the central values. Any extreme or outliers will not be relevant. In this question, it appears that 69.21 meters, the gold medal throw for women, is an outlier. This is because it is significantly higher than any of the other values. This outlier will skew the mean for women. It will be higher than it would otherwise have been if this value was not included.

We can therefore conclude that for women, there is one very high result in comparison to the rest of the data, which increases the mean but not the median. In general, an outlier will impact the mean far more than the median.