Page 8-19
Given the list of class marks S = {s
1
, s
2
, …, s
n
}, and the list of frequency
counts W = {w
1
, w
2
, …, w
n
}, the weighted average of the data in S with
weights W represents the mean value of the grouped data, that we call s, in
this context:
N
sw
w
sw
s
n
k
kk
n
k
k
n
k
kk
∑
∑
∑
=
=
=
⋅
=
⋅
=
1
1
1
,
where
∑
=
=
n
k
k
wN
1
represents the total frequency count.
The mean value for the data in lists S and W, therefore, can be calculated
using the procedure outlined above for the weighted average, i.e.,
We’ll store this value into a variable called XBAR:
The variance of this grouped data is defined as
N
ssw
w
ssw
V
n
k
kk
n
k
k
n
k
kk
∑
∑
∑
=
=
=
−⋅
=
−⋅
=
1
2
1
1
2
)()(
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