augustus021 wrote:
A set of data consists of the following 5 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
A. -1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8
Hi guys, can you help me understand when to use N-1 (sample variance)/N (population variance) in the denominator of the variance equation
I see that in this question, using sample variance equation will give us answer E
While using population variance equation will give us answer D (OA)
Sample standard deviation of {0, 2, 4, 6, 8} (original set), with N - 1 in the denominator, is \(\sqrt{10}≈3.16\)
Sample standard deviation of {0, 2, 4, 6, 8, -1, 9} (option A), with N - 1 in the denominator, is \(\sqrt{5}≈3.9\)
Sample standard deviation of {0, 2, 4, 6, 8, 4, 4} (option B), with N - 1 in the denominator, is \(2\sqrt{\frac{5}{3}}≈2.58\)
Sample standard deviation of {0, 2, 4, 6, 8, 3, 5} (option C), with N - 1 in the denominator, is \(\sqrt{7}≈2.65\)
Sample standard deviation of {0, 2, 4, 6, 8, 2, 6} (option D), with N - 1 in the denominator, is \(2\sqrt{2} ≈ 2.83\)
Sample standard deviation of {0, 2, 4, 6, 8, 0, 8} (option E), with N -1 in the denominator, is \(2\sqrt{3} ≈ 3.46\)
B < C < D < Original < E < A. But E is closer to the original than D.
Population standard deviation of {0, 2, 4, 6, 8} (original set), with N in the denominator, is \(2\sqrt{2}≈2.83\)
Population standard deviation of {0, 2, 4, 6, 8, -1, 9} (option A), with N in the denominator, is \(3\sqrt{\frac{10}{7}}≈3.6\)
Population standard deviation of {0, 2, 4, 6, 8, 4, 4} (option B), with N in the denominator, is \(2\sqrt{\frac{10}{7}}≈2.39\)
Population standard deviation of {0, 2, 4, 6, 8, 3, 5} (option C), with N in the denominator, is \(\sqrt{6}≈2.44\)
Population standard deviation of {0, 2, 4, 6, 8, 2, 6} (option D), with N in the denominator, is \(4\sqrt{\frac{3}{7}}≈2.62\)
Population standard deviation of {0, 2, 4, 6, 8, 0, 8} (option E), with N in the denominator, is \(6\sqrt{\frac{2}{7}}≈3.2\)
B < C < D < Original < E < A. But D is closer to the original than E.
So, yes, you're correct. Depending on the formula used, you will get different answers. It's worth noting that "the standard deviation" on the GMAT refers to the population standard deviation. However, you you don't really need to know this and you won't need to calculate standard deviations on the GMAT. Instead, you need to understand the concept of standard deviation: GMAT questions on this topic are more conceptual than computational. The main thing you should know about standard deviation is that it measures the variation or dispersion of data points from the mean. A low standard deviation indicates that the data points are closely clustered around the mean, while a high standard deviation suggests that the data points are spread out over a larger range of values.
Therefore, the question above is NOT at all a realistic representation of what you would get on the GMAT, and it might not be worth your time to focus on it.