SOLUTION: for the following data set, approximate the sample standard deviation.
miles (per day)---Frequency
1-2----------- --- 9
3-4----------- --- 22
5-6----------- --- 28
7-8----
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Probability-and-statistics
-> SOLUTION: for the following data set, approximate the sample standard deviation.
miles (per day)---Frequency
1-2----------- --- 9
3-4----------- --- 22
5-6----------- --- 28
7-8----
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Question 332582: for the following data set, approximate the sample standard deviation.
miles (per day)---Frequency
1-2--------------- 9
3-4--------------- 22
5-6--------------- 28
7-8--------------- 15
9-10-------------- 14 Answer by jrfrunner(365) (Show Source):
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...
---
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
---
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.
---
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
