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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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