Weighted standard deviation

R

rohb

New Member
Joined
Feb 20, 2008
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6
Hi all,
I am having hardtime to calculate the weighted standard deviation. I have different values in column A and its weight in Colum B. How can i calculate WSD of the values considering the weightage of each value. That would be great if anyone could suggest the solution. Thanks in advance.

Rohb

<TABLE style="WIDTH: 96pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=128 border=0><COLGROUP><COL style="WIDTH: 48pt" span=2 width=64><TBODY><TR style="HEIGHT: 15pt; mso-height-source: userset" height=20><TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 48pt; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" width=64 height=20>Value</TD><TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 48pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=64>Weight</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>0.15</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.22</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>0.65</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.54</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>2.5</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.14</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>6</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.04</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>12</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.03</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>23.5</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.02</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>77.5</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.00</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>124</TD><TD class=xl64 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">0.00</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD class=xl63 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.95pt; BACKGROUND-COLOR: transparent" height=17>Sum
weight

</TD><TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">1.00</TD></TR></TBODY></TABLE>
 

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rohb said:
Hi all,
I am having hardtime to calculate the weighted standard deviation. I have different values in column A and its weight in Colum B. How can i calculate WSD of the values considering the weightage of each value. That would be great if anyone could suggest the solution. Thanks in advance.

Rohb

<TABLE style="WIDTH: 96pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=128><COLGROUP><COL style="WIDTH: 48pt" span=2 width=64><TBODY><TR style="HEIGHT: 15pt; mso-height-source: userset" height=20><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 15pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl65 height=20 width=64>Value</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl65 width=64>Weight</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>0.15</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.22</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>0.65</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.54</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>2.5</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.14</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>6</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.04</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>12</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.03</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>23.5</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.02</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>77.5</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.00</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl66 height=17>124</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl64>0.00</TD></TR><TR style="HEIGHT: 12.95pt; mso-height-source: userset" height=17><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 12.95pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl63 height=17>Sum
weight


</TD><TD style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8" class=xl67>1.00</TD></TR></TBODY></TABLE>
Click to expand...

Let A2:B9 house the data. The following formula

=SQRT(SUMPRODUCT((A2:A9-AVERAGE(A2:A9))^2,B2:B9)/(((SUM(COUNTIF(B2:B9,{"<0",">0"}))-1)*SUM(B2:B9))/SUM(COUNTIF(B2:B9,{"<0",">0"}))))

attempts to map the definition given in

http://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf
 
Upvote 0
Hi Aladin,

thanks for your contribution, though by the definition in
http://www.itl.nist.gov/div898/softw...2/weightsd.pdf
the following formula have to use WEIGHTED mean instead of simple AVERAGE(A2:A9). The formula of weighted mean is by
http://www.itl.nist.gov/div898/softw...2/weigmean.pdf
SUMPRODUCT(B2:B9;A2:A9)/(SUM(B2:B9))

and then complete formula is

=SQRT(SUMPRODUCT((A2:A9-SUMPRODUCT(B2:B9;A2:A9)/(SUM(B2:B9)))^2;B2:B9)/(((SUM(COUNTIF(B2:B9;{"<0",">0"}))-1)*SUM(B2:B9))/SUM(COUNTIF(B2:B9;{"<0";">0"}))))
 
Upvote 0
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