The numbers of members in 6 yoga clubs are 76, 70, 73, 67, 71, and 87. Suppose a person in the club with 87 members transfers to the club with 67 members. A student claims
that the measures of center and the measures of spread will all change. Correct the student's error.
There are 6 elements in the set, so the IQR is the difference between the (select) v element and the
(select) . The only values that are changing are the (select) v. This will not affect the IQR.
The median is the average of the (select) v elements and likewise remains unchanged. The mean
will also remain unchanged because the sum of all the elements doesn't change. The range will change
from 20 to
The standard deviation will also (select)
because the value of
both the first and last elements will be closer to the mean.