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Chapter 18: A. Basic Statistics and Applications 203
EXAMPLE 18.3
To illustrate this method we consider a simple example. The following data give the
length of an alignment pin for a printer shaft in a batch of production:
Find the median alignment pin length.
Solution:
30, 24, 34, 28, 32, 35, 29, 26, 36, 30, 33
Step 1. Write the data in ascending order and rank them from 1 to 11 since
n = 11.
Observations in ascending order: 24 26 28 29 30 30 32 33 34 35 36
Ranks: 1 2 3 4 5 6 7 8 9 10 11
Step 2. Find the rank of the median.
Rank of the median = (n + 1)/2 = (11 + 1)/2 = 6
Step 3. Find the value corresponding to rank 6 (this is the rank of
the median).
The value corresponding to rank 6 is 30.
Thus, the median alignment pin length is M d = 30. This means that at the most 50
percent of alignment pins are of length less than 30 and at the most 50 percent are of
length greater than 30.
EXAMPLE 18.4
The following data describe the sales (in thousands of dollars) for 16 randomly selected
sales personnel distributed throughout the United States:
10, 8, 15, 12, 17, 7, 20, 19, 22, 25, 16, 15, 18, 250, 300, 12
Find the median sales of these individuals.
Solution:
Step 1. Observations in ascending order: 7 8 10 12 12 15 15 16 17 18 19 20 22
25 250 300
Ranks: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Step 2. Rank of the median = (16+1)/2 = 8.5
Step 3. Find the value corresponding to the 8.5th rank. Since the rank of the
median is not a whole number, in this case the median is defined as
the average of the values that correspond to the ranks 8 and 9 (since
rank 8.5 is located between the ranks 8 and 9).
The median of the above data is M d = (16 + 17)/2 = 16.5.
Thus, the median sales of the given individuals is sixteen thousand and five hundred
dollars.
Part IV.A.1