You can
put this solution on YOUR website!Since you dont have the exact value, but instead have a range of values
the first thing to do is to get a surrogate (proxy) value. This is usually set a the mid point of the interval
1.5
3.5
etc...
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next set up a data table as follows
Let X=midpoint, F=frequency
--
X ------ F ---- X*F
1.5 ----- 9 ---- 13.5
3.5 ----- 22 ---- 77.0
5.5 ----- 28 ---- 154.0
7.5 ----- 15 ---- 112.5
9.5 ----- 14 ---- 133.0
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Compute the average = Xbar =
--
for each interval compute a column (Xi-Xbar)^2
and then sum this column
=[(1.5-5.57)^2]*9 + [(3.5-5.57)^2]*22 +..+[(9.5-5.57)^2]*14 = 515.59
this sum represents the sum of squared deviations.
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Find the Variance
Variance =
=515.59/(88-1)=5.926
---
Standard dev = Sqrt(Variance) = Sqrt(5.926)=2.434
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There is another form of the variance formula that you could use
Variance =
