Читать книгу Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP - Bhisham C. Gupta, Irwin Guttman - Страница 69

We denote the median of a data set by . To determine the median of a data set of size , we take the following steps:

1 Step 1. Arrange the observations in the data set in an ascending order and rank them from 1 to .

2 Step 2. Find the rank of the median that is given by(2.5.3) We can check manually that the conditions of Definition 2.4.2 are satisfied.

3 Step 3. Find the value of the observation corresponding to the rank of the median found in (2.5.3). If denotes the th largest value in the sample, and if(i) odd, say , then the median is (ii) even, say , then the median is taken as

Note that in the second case, we take median as the average of and because both satisfy the two conditions of Definition 2.4.2, resulting in their mean being adopted as a compromise between these two values for the value of .

We now give examples of each case, odd and even.

Example 2.5.3 (Alignment pins for the case of n odd, ) The following data give the length (in mm) of an alignment pin for a printer shaft in a batch of production:

30, 24, 34, 28, 32, 35, 29, 26, 36, 30, 33

Find the median alignment pin length.