MAT 142
Lecture Video Series
Measures of Central
Tendency
Objectives
• Calculate the mean of a set of data.
• Calculate the median of a set of data.
• Calculate the mode of a set of data.
Vocabulary
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central tendency
summation notation
mean
median
mode
outlier
Formulas
x
x
x


n
f  x 


n
mean of ungrouped data
(here x is the data point)
mean of grouped data
(here x is the midpoint of a group)
Fran Tarkenton holds the all-time
record in professional football for
throwing touchdown passes. The
number of touchdown passes (TDs)
for each of his seasons is given in the
table. Find the mean, median, and
mode of the number of touchdown
passes per year thrown by Tarkenton
Year
TDs
Year
TDs
1961
18
1970
19
1962
22
1971
11
1963
15
1972
18
1964
22
1973
15
1965
19
1974
17
1966
17
1975
25
1967
29
1976
17
1968
21
1977
9
1969
23
1978
25
Tom Ball, an avid jogger, kept
detailed records of the number of
miles he ran per week during the past
year. The frequency distribution
summarizes his records. Find the
mean, median, and mode of the
number of miles per week that Tom
ran.
Miles run
per week
Number
of weeks
0
5
1
4
2
10
3
9
4
10
5
7
6
3
7
4
If your scores on the first four
exams in a class are 73, 67, 83, and
81, what score do you need on the
next exam for your overall mean to
be at least 70?
The ages of the women who gave birth in
the United States in 2006 are given in the
table below. Find the mean age of these
women.
Age
15 ≤
20 ≤
25 ≤
30 ≤
35 ≤
40 ≤
45 ≤
x < 20
x < 25
x < 30
x < 35
x < 40
x < 45
x < 50
Number of Women
442,000
1,081,000
1,812,000
950,000
499,000
105,000
7,000
The mean salary of ten employees
is $28,000, and the median is
$25,000. The highest paid
employee gets a $5,000 raise.
a. What is the new mean salary
of the ten employees?
b. What is the new median salary
of the ten employees?
Elizabeth Jones
for
The School of Mathematical and Statistical
Sciences
at
Arizona State University
Videographer
Mike Jones