Help 18,19

 Apr 25, 2018

In order to find the mean, find the sum of all the data points and divide by the number of data points. Since this is a "lunch expenditure for a week," I would assume that this is only a sample, so I will x bar as the mean.




Yet again, I am making the assumption that this data is a sample because that seems like a reasonable assumption. In order to find the standard deviation, this formula will provide that answer:


\( \text{SD}_{\text{sample}}=\sqrt{\frac{\Sigma_{i=1}^{n} (x_{i}-\overline{x})^2}{n-1}}\)


Now, this is a loaded formula! Let's first define a few variables:


\(x_i\) is the individual data point

\(\overline{x}\) is the average of the data set

\(n\) is the number of data points


Let's break this formula down. There are 5 steps, one of which we have already done. 


  • Find the mean
  • For every data point, subtract the mean from it. Then, square it.
  • Sum the values from step 2
  • Divide by the number of data points minus 1
  • Take the square root of the result

I will show the work with a table. This takes care of steps 2 and 3 simultaneously. 


  Day \(x_i\) \(x_i-\overline{x}\) \((x_i-\overline{x})^2\)  
  Monday 4.85 -0.25 0.0625  
  Tuesday 5.10  0.00 0.0000  
  Wednesday 5.50  0.40 0.1600  
  Thursday 4.75 -0.35  0.1225  
  Friday 4.50 -0.60 0.3600  
  Saturday 5.00 -0.10 0.0100  
  Sunday 6.00  0.90 0.8100  
Total       1.5250  


Now, I will do the remaining steps.




The variance is just the square of the standard deviation. 




19) Picking a random number, say 2932, is independent to a coin flip; one has no effect on the other. 

 Apr 25, 2018

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