MHB Sample & Population Variance & SD Review

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When calculating standard deviation (SD) and variance for a given sample of values, it's essential to use the sample formulas rather than the population formulas. Since the data provided is a sample, the sample SD and variance should be calculated to reflect the characteristics of that specific subset. The distinction is crucial because population calculations assume access to the entire data set, which is not the case here. Thus, the correct approach is to focus solely on the sample data for these calculations. Understanding this difference is vital for accurate statistical analysis.
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Reviewing for finals when given a sample of a 8 values {1,2,3,4,5,6,7,8} , when solving for the SD and the variance do I solve for the population variance and SD OR since the question states that it is a sample you solve for the sample SD and variance
 
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Tacking for granted that SD stand for standard deviation, since you only have a sample there is no way for you to evaluate the SD/variance of the whole population.

Therefore you solve the SD/variance for the sample only.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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