1.3. Measures of Center http://www.ck12.org
Other measures of center include themidrange, which is the mean of the maximum and minimum values. In an
n%trimmed mean, you remove a certain percentage of the data (half from each end) before calculating the mean. A
weighted mean, involves multiplying individual data values by their frequencies or percentages before adding them
and then dividing by the total of the weights.
Apercentileis a data value in which the specified percentage of the data is below that value. The median is the 50th
percentile. Two well-known percentiles are the 25thpercentile, which is called thelower quartile(LQorQ 1 ), and
the 75thpercentile, which is called theupper quartile(U QorQ 3 )
Points to Consider
- How do you determine which measure of center best describes a particular data set?
- What are the effects of outliers on the various measures of spread?
- How can we represent data visually using the various measures of center?
Review Questions
- In Lois’ 2nd−grade class, all of the students are between 45 and 52 inches tall, except one boy, Lucas, who is
62 ′′inches tall. Which of the following statements is true about the heights of all of the students?
a. The mean height and the median height are about the same
b. The mean height is greater than the median height.
c. The mean height is less than the median height.
d. More information is needed to answer this question.
e. None of the above is true. - Enrique has a 91, 87 ,and 95 for his statistics grades for the first three quarters. His mean grade for the year
must be a 93 in order for him to be exempt from taking the final exam. Assuming grades are rounded following
valid mathematical procedures, what is thelowestwhole number grade he can get for the 4thquarter and still
be exempt from taking the exam? - How many data points should be removed fromeach endof a sample of 300 values in order to calculate a
10% trimmed mean?
a. 5
b. 10
c. 15
d. 20
e. 30 - In the last example, after removing the correct numbers and summing those remaining, what would you divide
by to calculate the mean? - The chart below shows the data from the Galapagos tortoise preservation program with just the number of
individual tortoises that were bred in captivity and reintroduced into their native habitat.
TABLE1.4:
Island or Volcano Number of Individuals Repatriated
Wolf 40
Darwin 0
Alcedo 0