//  File MIT-Lab-26-03-00-05.txt. Edition 2-26-2020.


//  Title
      Estimating_the_Variance_-_First_Try
//  Data file
      KeyWestLows.dat
//  List of Sample Sizes
      1 40 1 5


// Problem Specs
//	SampleSize 
//      PauseCheckbox(-1 checked 0 cleared)
//      EstMeanOrVar (-1 if Mean only    +1 Var only   0 both Mean and Var)
//      ShowToFrom (-1 show 0 don't show)
//      DefaultVarEstBasedOnActOrEst (-1 Act  0 Est)
//      DefaultVarEstDivisor (-1 T  0 T-1)


` 4 0 1  0  -1 -1
Objective: Show that our first estimation procedure for the population variance is unbiased:
_______Calculate the deviation from the actual mean, ActMean.
_______Square the deviation.
_______Sum the squared deviations.
_______Divide the sum of squared deviations by the sample size, T.
_
Two new fields have now appeared in the simulation:
___Use Mean: Act selected to calculate the deviations from actual mean.
___Divide by: T selected to divide by the sample size.



`
Note that the Estimate Variance checkbox is checked; the simulation will estimate
 the population variance.
_
By default, the sample size equals 4. Be certain the the Pause checkbox is cleared.
_
1. Click Start and then after many, many repetitions click Stop. What is the mean
 (average) of the variance estimates? 
_
2. Is our first estimation procedure for the population variance unbiased? Explain.
`
3. This procedure appears to be exactly what we are looking for. But in reality, this procedure does not help us. Explain.