HP 50G, User Manual

Page: 274 / 887

Page 8-17
Thus, the geometric mean of list S is s
g
= 1.003203…
Weighted average
Suppose that the data in list S, defined above, namely:
S = {1,5,3,1,2,1,3,4,2,1}
is affected by the weights,
W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
If we define the weight list as W = {w
1
,w
2
,…,w
n
}, we notice that the k -th
element in list W, above, can be defined by w
k
= k. Thus we can use function
SEQ to generate this list, and then store it into variable
@@@W@@@
as follows:
Given the data list {s
1
, s
2
, …, s
n
}, and the weight list {w
1
, w
2
, …, w
n
}, the
weighted average of the data in S is defined as
.
To calculate the weighted average of the data in list S with the weights in list W,
we can use th e following steps:
1. Multiply lists S and W:
2. Use function
Σ
LIST in this result to calculate the numerator of s
w
:
∑
∑
=
=
⋅
=
n
k
k
n
k
k k
w
w
s w
s
1
1