Eight sales closed at $200,000, $220,000, $220,000, $220,000, $230,000, $230,000, $250,000 and $270,000. The mean is $230,000. What is the population standard deviation?
Correct Answer
B) $20,000
Why this is correct: The original explanation provides the calculation: squared deviations total 3,200 (in thousands of dollars). Variance = 3,200 / 8 = 400. Standard deviation = √400 = 20, so $20,000. The governing concept is that population standard deviation measures dispersion of all data points around the mean. Step-by-step: 1) Find deviations from mean ($230k): (-30, -10, -10, -10, 0, 0, 20, 40) in $1,000s. 2) Square each: (900, 100, 100, 100, 0, 0, 400, 1600). 3) Sum: 3200. 4) Divide by N (8): 400. 5) Square root: 20 ($20,000). Why the other choices are wrong: $16,000 might result from an incorrect divisor or mis-calculation. $24,000 could be the result of using sample standard deviation formula (dividing by n-1). $40,000 is the range ($270k - $200k = $70k), not the standard deviation. Exam tip: For population standard deviation, divide the sum of squared deviations by N (number of data points), then take the square root.
Why This Is the Correct Answer
Why this is correct: The original explanation provides the calculation: squared deviations total 3,200 (in thousands of dollars). Variance = 3,200 / 8 = 400. Standard deviation = √400 = 20, so $20,000. The governing concept is that population standard deviation measures dispersion of all data points around the mean. Step-by-step: 1) Find deviations from mean ($230k): (-30, -10, -10, -10, 0, 0, 20, 40) in $1,000s. 2) Square each: (900, 100, 100, 100, 0, 0, 400, 1600). 3) Sum: 3200. 4) Divide by N (8): 400. 5) Square root: 20 ($20,000). Why the other choices are wrong: $16,000 might result from an incorrect divisor or mis-calculation. $24,000 could be the result of using sample standard deviation formula (dividing by n-1). $40,000 is the range ($270k - $200k = $70k), not the standard deviation. Exam tip: For population standard deviation, divide the sum of squared deviations by N (number of data points), then take the square root.
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