# W13D25 Measures of Central Tendency

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STEM     LEAVES

4 23 6 6 7 8 9 9
5 00 1 1 1 1 2 2 4 4 4 4 4 5 5 5 5 6 6 6 7 7 7 7 8

6 01 1 1 2 4 4 5 8 9

May 10, 2010                  Math 132: Foundations of Mathematics
Math 132:
Foundations of Mathematics

Amy Lewis
Math Specialist
IU1 Center for STEM Education

May 10, 2010                       Math 132: Foundations of Mathematics
12.2 Measures of Central Tendency
• Determine the mean, median, mode, and
midrange for a particular data set

May 10, 2010             Math 132: Foundations of Mathematics
Measures of Central Tendency
• Mean – the sum of the data items divided
by the number of items.
• Median – the data item in the middle of an
ordered data set.
• Mode – the data value that occurs most
often in a data set.
• Midrange – the mean of the lowest and
highest data values.
May 10, 2010               Math 132: Foundations of Mathematics
Military Expenditures
National Expenditure     •Calculate the MEAN
Country
(billions of dollars)
and MEDIAN of this
USA                      417.4
data set.
Japan                   46.9
UK                      37.1             •What is the
France                  35.0             MIDRANGE of the data
China                   32.8             set?
Germany                 27.2
•Describe why one of
Italy                   20.8
the measures of central
Iran                    19.2
tendency is so much
Saudi Arabia            19.1
greater than the other.
South Korea             13.9
May 10, 2010                              Math 132: Foundations of Mathematics
Frequency Distributions
• The following data represents the age at
inauguration for the 20th century presidents (up
to George W. Bush).
• Find the MEAN, MEDIAN, MODE, and MIDRANGE
of the data set.

x 42 43 46 51 52 54 55 56 60 61 64 69
f 1 1 1 3 1 2 2 2 1 2 1 1

May 10, 2010                  Math 132: Foundations of Mathematics
are:
51, 69, 78, 86, 86, 92
measure of central tendency?
• What argument would you make to the
teacher for the grade you want?
May 10, 2010                Math 132: Foundations of Mathematics
Using Data Displays
• Look at #51 on page 703.
• Calculate the MEAN, MEDIAN, MODE, and
MIDRANGE for the data presented.

May 10, 2010                Math 132: Foundations of Mathematics
Candy Sales
• The members of a local organization are
raising money by selling candy bars at
several locations on the weekends. After
the first weekend, they collected the
number of candy bars sold by each
member.

May 10, 2010               Math 132: Foundations of Mathematics
Candy Sales
• Display the data in a stem-
24            27   40     and-leaf plot.
38            29   38
• Use measures of central
50            35   37     tendency to report on the
33            38   41     sales from the first
29            60   53     weekend.
37            44   48   • What changes would you
43            28   42     make for the second
weekend?
May 10, 2010                       Math 132: Foundations of Mathematics
Homework
Page 703: 55-58

Next Session: Tuesday, May 11

May 10, 2010             Math 132: Foundations of Mathematics

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