We may be in a situation where one datum apparently has a strong influence on the mean of a data set.

Consider the data set:

The 69.2 datum appears to be out of class, e.g., it comes from a different population.

Notice how this number affects the calculated means:

Since the mean obtained using 69.2 is very different from the majority of the data, we suspect it is out of class.

The Q-test is often used to test this hypothesis. Like Student's t-test, we calculate a Q value under the null hypothesis, e.g., data are the same, and then compare it to a table value using the logical scheme

In the later event, we should reject the data.

The Q value is calculated using:

where the GAP is the difference between the suspect datum and its nearest neighbor and the RANGE is the difference between the maximum and minimum data in the set.

Rearranging the data set in order from the minimum to the maximum:

The RANGE and GAP are:

and the calculated Q value is:

We look into the table of Q values for the number of measurement data. In this case, N=6 and Q_table=0.56 Since

the null hypothesis is wrong, and we should reject the datum 69.2 from the set.