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STA2023  Chapter 4b (Describing Distributions Numerically)
Measures of Center:
1.
The
Mean
is the “average” of the data values
_
y
Total
y
Number of Observations
n
=
=
⋅
⋅
∑
2.
The
Median
is the middle value in the data set:
M =
1
2
n
+
(this formula finds the location of the median)
3.
The
Mode
is the most frequently occurring data value
4.
The
Midrange
is the average of the lowest and highest data values
2
Low
High
+
Deciding on which measure of centering is most appropriate for a given data set depends on the data’s
distribution. (see the highlighted text on page 63)
*
The mean and midrange are not stable measures of centering (they are highly affected by skewing
and/or outliers)
*
The median and mode are stable measures of centering (not greatly affected by skewing or outliers)
Think about the U.S. census data on household incomes.
Does the census report mean household income or
median household income?
Why?
Activity 1 (data set from page 80, #24):
Here are the annual numbers of deaths from tornadoes in the United States from 1990 through 2000.
53
39
39
33
69
30
25
67
130
94
40
A. Find the mean
(average) number of tornado deaths in the U.S. from 1990 through 2000.
B. Find the median
number of tornado deaths in the U.S. from 1990 through 2000.
Hint: first reorder the data from smallest to largest, then use the formula
M =
1
2
n
+
25
30
33
39
39
40
53
67
69
94
130
Note: In this data set,
n
is an odd number and the median turned out to be one of the values in the data set
(M = 40).
If
n
is even, the median will be the midpoint between the two middle values in the data set.
Let’s say that the given data set did not include y = 130 (thus,
n
= 10)
The location of the median in the ordered data set is:
M = (10 + 1)/2 = 5.5
Thus the median is halfway between the 5
th
and 6
th
data values in the ordered data set (M = 39.5)
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C. A graph will help you to determine whether to use the mean or median to describe the center of this
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 Spring '08
 Ripol
 Statistics

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