QMS 102 Weighted Mean
Imagine the world consisted of 5 cities with
populations of 1 to 5 as indicated.
Suppose some “politicians”
decided to split the world into two countries A and B
as indicated.
What is the mean size of a city?
QMS 102 Weighted Mean
:A = 2.666666 NA = 3
:B = 3.5 NB = 2
a]
What is the mean size of a city?
b]
What is the mean size of a country’s city?
a] : = (2.6666 x 3 + 3.5 x 2) / (3 + 2) = 3
b] : = ( 2.666666 + 3.5 ) / 2 = 3.08
Note that the weighted mean is just the usual mean but the data has been provided
in some summary format.
When the Central Canada unemployment rate is reported each month, is it a (weighted) average or is it a provincial average?
Province
10.64%
10.71%
10.5%
Total
Population
(millions)
Employable
Residents
(millions)
Provincial Unemployment Rate
Que
6
4
12%
Ont
5
3
9%
(using total population as weight),
( using employable residents as weights) or
(unweighted) ?
In Toronto there are lots of hotdog venders in High Park. Below is a list of their prices and the number of hot dogs they each sold on July
7th.
a] What is the mean hotdog price on July7th ? [$1.5625]
b] What was the mean revenue of a hotdog sold on July 7th ? [$1.225]
High Park Hotdog Sells
July 7th
Vender
Hotdog Price
Hotdogs Sold
A
$1.00
225
B
$1.50
50
C
$1.25
200
D
$2.50
25
List1: 1, 1.5,......
List2: 225, 50,...
[stat][calc][set]
1-var List “List1" values/midpoints/means
1-var Freq “List2" frequencies/weights
[exit][1-var]
The frequency distributions of the number of days spent in the hospital for burn victims in two different treatment centres is shown
below.
# of Patients
Number of Days
Centre A
Centre B
0 and under 5
16
11
5 and under 10
20
24
10 and under 15
34
42
15 and under 20
14
7
20 and under 25
16
16
Which centre had the longest stays?
Which centre has the more variable length of stay?
Midpoint
Number of Days
Centre A
Centre B
2.5
0 and under 5
16
11
7.5
5 and under 10
20
24
12.5
10 and under 15
34
42
17.5
15 and under 20
14
7
22.5
20 and under 25
16
16
Calculator Centre A
List1
List 2
1
2.5
16
2
7.5
20
3
12.5
34
4
17.5
14
5
22.5
16
6
-------
-------
[stat][calc][set]
1-var List “List1" values/midpoints/means
1-var Freq “List2" frequencies/weights
[exit][1-var]
Mean length of stay at Centre A is 12.2 days with a standard deviation of 6.3889 days.
The coefficient of variation (CV) of the length of stay at Centre A is s/0 = 6.3889/12.2=
52.4%
Centre B? [12.15, 5.914, 100 ; 48.7%]
)