When you have completed this chapter, you will be able to: Calculate the arithmetic mean, the weighted mean, the median, the mode, and the geometric mean of a given data set; identify the relative positions of the arithmetic mean, median and mode for both symmetric and skewed distributions; point out the proper uses and common misuses of each measure; explain your choice of the measure of central tendency of data; explain your choice of the measure of central tendency of data.
Trang 13 1
Trang 21. Calculate the arithmetic mean, the weighted mean, the median,
the mode, and the geometric mean of a given data set.
2. Identify the relative positions of the arithmetic mean , median
and mode for both symmetric and skewed distributions
When you have completed this chapter, you will be able to:
Explain your choice of the measure of central tendency of data.
3. Point out the proper uses and common misuses of each
measure
4.
5. Explain the result of your analysis.
Trang 3The average price of a house in Toronto in 1996 was $238,511 (StatCan)
My grade point average My grade point average for last semester was 4.0
Trang 4Arithmetic Mean Arithmetic Mean
All values are used
It is unique
The sum of the deviations from the mean is 0
It is calculated by summing the values and
dividing by the number of values
It requires the interval scale
…is the most widely used measure of location.
Trang 5Population Mean Population Mean
x N
Trang 10Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved.
Properties of an Arithmetic Mean
Properties of an Arithmetic Mean
tendency where the sum of the deviations
of each value from the mean is zero!
…The mean is affected by unusually
large or small data values
Trang 15See See INPUT NEEDS
INPUT NEEDS
A3:A42
Click on
OK
Trang 16Using
See Solution See Solution
Alternate solution…
Trang 17CLICK ON CLICK ON PASTE FUCTION PASTE FUCTION
CLICK ON
See See
Trang 18See… SCROLL DOWN TO STATISTICAL SCROLL DOWN TO STATISTICAL
Trang 19Click on
OK
HIGHLIGHT AVERAGE IN RIGHT MENU HIGHLIGHT AVERAGE IN RIGHT MENU
See See
Trang 21The weighted mean of a set of numbers
x1, x2, xn,
with corresponding
weights w1, w2, ,wn, is computed from the following formula:
n n w
Trang 2289 0
$ 50
50 44
$
) 50 0 ($
15
) 90 0 ($
15
) 75 0 ($
15
w
μ
During a one hour period on a hot Saturday afternoon cabana boy Chris served fifty drinks.
the weighted mean of the price of the drinks
Trang 23There are as many values above the median as below it in the data
Trang 24The ages for a sample of five college students are:
21, 25, 19, 20, 22
The heights of four basketball players, in inches, are:
Trang 25intervallevel, and ordinallevel data
It can be computed for an openended frequency distribution
if the median
Trang 26The Mode
The Mode
is the value of the observation
that appears most
frequently used The exam scores for ten students are:
81, 93, 84, 75,
68, 87, 81, 75, 81, 87
The score of 81 occurs the most often
…it is the Mode!
Trang 27The Geometric Mean ( GM ) of a set of n numbers is defined as the nth root of the product of the n numbers.
The geometric mean is used to average percents, indexes, and relatives.
The formula is:
Geometric Mean
Trang 28The interest rate on three bonds was
5, 21, and 4 percentThe Geometric Mean is:
Geometric Mean
49
7 )
4 )(
21 )(
5 (
Trang 29Another use of the geometric mean is to determine the percent increase in sales, production or other business or economic series
Trang 30The total number of females enrolled in American
colleges increased from 755,000 in 1992 to 835,000 in 2000.
The total number of females enrolled in American colleges increased from 755,000 in 1992 to 835,000 in 2000.
0127
1 000
, 755
000 ,
Trang 31Determining the Median, Mode or Geometric Mean
in Excel
Trang 32Click on Tools
Trang 33Highlight
DESCRIPTIVE
Trang 34The
geometric mean
doesn’t show up in
summary statistics!
Trang 35CLICK ON CLICK ON PASTE FUCTION PASTE FUCTION
CLICK ON
See See
Trang 36SCROLL DOWN
to STATISTICAL
SCROLL DOWN
to
STATISTICAL
See…
Trang 37Using
HIGHLIGHT MEDIAN
IN RIGHT MENU
HIGHLIGHT MEDIAN
IN RIGHT MENUSee See
Trang 38See See
OR…
HIGHLIGHT
GEOMETRIC MEAN
IN RIGHT MENU
HIGHLIGHT
GEOMETRIC MEAN
IN RIGHT MENU
Trang 39See See
HIGHLIGHT MODE
IN RIGHT MENU
HIGHLIGHT MODE
IN RIGHT MENU
Trang 41Source: Statistics Canada, Tourism and the Centre for Education Statistics
Source: Statistics Canada, Tourism and the Centre for Education Statistics
Trang 43The mean is strongly affected by the inclusion of
these two OUTLIERSThe mean is strongly affected by the inclusion of
these two OUTLIERS
Trang 44in a frequency distribution is computed by the following formula:
N
fx
x
Trang 45A sample of ten movie theatres in a metropolitan
area tallied the total number of movies showing last week.
Trang 46Continued…
6610
Total
3010
3
9 to under 11
88
1
7 to under 9
186
3
5 to under 7
84
2
3 to under 5
22
1
1 to under 3
(f)(x)
Class Midpoint
The Mean
fx x
Trang 47= 6.6 66
Continued…
(f)(x)
Class Midpoint
The Mean
fx x
Trang 48610
6532.5
137.527.5
13522.5
21017.5
62.512.5
30Total
The Mean
fx x
= 20.3330
610
Formula
N fx
x
Trang 50)(
Trang 51Cumulative
f
71
7 to under 9
63
5 to under 7
32
3 to under 5
11
Trang 523 52The Mode of Grouped Data The Mode of Grouped Data
The mode for grouped data is approximated by the
midpoint of the class with the largest class frequency
103
9 to under 11
81
7 to under 9
63
5 to under 7
42
3 to under 5
21
1 to under 3
Class Midpoint
Frequency
f
Movies Showing
This is considered
to be
BiModal
This is considered
to be
BiModal
Trang 53Approximate the Mode of this distribution
27.522.517.512.5
Frequency
f
Hours Studying
The modal class is 15 to under 20,
approximately 17.5
The modal class is 15 to under 20 ,
approximately 17.5
Trang 56< Median
Mean
Trang 57searchable glossary access to Statistics Canada’s EStat data
…and much more!
Trang 58This completes Chapter 3