Читать книгу Medical Statistics - David Machin - Страница 43

Consider the following 16 corn sizes in millimetres selected randomly from the Farndon (2013) study. We order the 16 observations from smallest to largest (See Table 2.4); the median is the middle observation which splits the data set into two halves with equal number of observations in each half (eight in this example). As the number if observations are even (n = 16); the median is the average of the two central ordered values (the eighth and ninth). So, the median corn size is (3 + 3)/2 = 3 mm.

If we had observed an additional 17th subject with a corn size of 10 mm the median would be the 9th ordered observation, which is 3 mm.

The median has the advantage that it is not affected by outliers, so for example the median in the data would be unaffected by replacing largest corn size of ‘10 mm’ with ‘100 mm’. However, it is not statistically efficient, as it does not make use of all the individual data values.