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Section 3.1
Measures of Center
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
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3.1 Measures of Center
• A measure of central tendency
describes a central, or typical, value in
a data set.
• The mean, median, and mode are all
measures of central tendency.
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Calculating the Mean:
• The mean is what we typically call the
“average” of a data set.
• To calculate the mean, simply add all the
values and divide by the total number in the
data set.
• Formula:
It is possible for the mean not to be a number in the data set.
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Calculate the sample mean of the following heights in inches:
63 68 71 67 63 72 66 67 70
Solution:
When calculating the mean, round to one more decimal place than
what is given in the data.
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Calculating the median:
• The median is the middle value in an
ordered set.
• To calculate the median, first put the
numbers in numerical order. Then,
a. if n is odd, the median is the number in
the center.
b. if n is even, the median is the mean of
the center two numbers.
It is possible for the median not to be a number in the data set.
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Calculate the median of the following sets of data:
a. 15 16 11 22 19 10 17 22
Solution:
10 11 15 16 17 19 22 22
b. 2.6 3.3 5.0 1.8 0.7 2.2 4.1 6.1 6.7
Solution:
0.7 1.8 2.2 2.6 3.3 4.1 5.0 6.1 6.7
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Calculating the mode:
• The mode is the data value(s) that occur(s)
most frequently.
• A data set may have one mode (unimodal),
two modes (bimodal), or many modes
(multimodal).
• If each data value occurs the same number
of times, then there is no mode.
The mode will always be a number in the data set.
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Calculate the mode of each data set:
a. 63 68 71 67 63 72 66 67 70
Solution:
63 68 71 67 63 72 66 67 70
b. 51 77 54 51 68 70 54 65 51
Solution:
51 77 54 51 68 70 54 65 51
c. 1 5 7 3 2 0 4 6
Solution:
No mode
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Which measure of the “average” is the best to use?
This all depends on the data:
• For qualitative data, the mode should be used.
• For quantitative date, the mean should be
used unless the data set contains outliers.
• Quantitative data sets with outliers should use
the median.
HAWKES LEARNING SYSTEMS
Numerical Descriptions of Data
math courseware specialists
3.1 Measures of Center
Choose the best measure of center for the following data sets:
a. The average t-shirt size (S, M, L, XL) of
American women.
Mode
b. The average salary for a professional team of
baseball players.
Median
c. The average price of houses in a subdivision
of similar houses.
Mean