WEEK 3: MEASURES OF CENTER
Complete this guide
on your computer
as you read.
CHAPTER 3: SECTIONS 3A & 3B
In the previous chapter we analyzed data frequency distribution, but here we are interested in the
values that the data set tends to center around (CENTRAL TENDENCY), discrepancies within
the data set or changes over time (VARIATION) and the position of a specific value within a set
(RELATIVE STANDING).
Read chapter 3 as you complete your class notes. To check to see if
you understand the concepts you can check your Student’s Solution Manual for the odd
numbered examples. Your TH3 assignment will incorporate some of the examples used in the
class notes.
3.2 MEASURES OF CENTER
MEAN
The most well known central measure of tendency is the
mean
(also informally known as the
average).
The formula for the mean is shown below.
x
x
n
=
∑
NOTE:
1.
The symbol
x
represents the mean.
2.
Each x represents a single data element.
3.
The
Σ
x means to sum up all the data elements.
4.
The n represents the total number of data elements
So, the formula says to add up all the individual data elements and divide that sum by the number
of elements.
If you have the data elements [3,4,5,6] for example, the sum would be 3+4+5+6
=18; the n would be 4 and the mean would be 18/4 = 6
325
Find the mean of 53,52,75,62,68,58,49,49. Use a calculator and show your work.
x
x
n
=
∑
Σ
x
=
n
=
Σ
x/n
=
x
=
326
Find the mean of 3,24,30,47,43,7,47,13,44,39. Use a calculator. Show your work.
x
x
n
=
∑
Σ
x
=
n
=
Σ
x/n
=
x
=
Is the cereal sugar content MEAN representative of American consumption?
Why?
1
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MEDIAN
Another well known central measure of tendency is the
median
which is the middle
value after the data elements are sorted from lowest to highest.
Example 1

Find the median of
3 4 1 2 9 2 8.
•
First, sort the data from lowest to highest:
1 2 2
3
4 8 9
•
Then, since 3 is the middle element, so the median of the set of data is
3
.
•
Notice that this is not an average, but just the number in the middle of the set.
Now we will add another element to our original set to give us an
even
number of points.
Example 2

Find the median of
3 4 1 2 9 2 8 5.
•
First we sort the data: 1 2 2
3 4
5 8 9.
•
Find the middle TWO values
3
4
•
Now, find the mean of those values.
x
= (3 + 4) / 2
= 7/2 = 3.5.
•
The median of the set of data is now
3.5
So, to find the median of a set of data with an
odd
number of elements, sort the data and
locate the middle number.
For data with an
even
number of elements, sort the data,
locate the two middle numbers, and then, find the mean of those two numbers.
325
Find the median of
53,52,75,62,68,58,49,49.
Reorder the data:
Median numbers:
Average of median numbers:
326
Find the median of 3,24,30,47,43,7,47,13,44,39.
Reorder the data:
Median numbers:
Average of median numbers:
Is the cereal sugar content MEDIAN representative of American consumption?
Why?
MODE
A third central measure of tendency is the
mode (M)
which is the value in the data that
repeats most frequently.
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 Spring '09
 MoSeKim
 Standard Deviation, Mean

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