In a dataset with n=50, standard deviation 8. If you add a data point at 24, how does the mean shift? Original mean is 50.

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Multiple Choice

In a dataset with n=50, standard deviation 8. If you add a data point at 24, how does the mean shift? Original mean is 50.

Explanation:
When you add a new data point, the mean becomes (n·mu + x) / (n + 1), so the shift is (x − mu) / (n + 1). Here, the original mean mu is 50, n is 50, and the new point x is 24. The shift is (24 − 50) / 51 = −26/51 ≈ −0.5098. The new mean is 50 + (−0.5098) ≈ 49.49. So the mean decreases by about 0.51, moving to approximately 49.49. The standard deviation doesn’t affect the mean shift.

When you add a new data point, the mean becomes (n·mu + x) / (n + 1), so the shift is (x − mu) / (n + 1). Here, the original mean mu is 50, n is 50, and the new point x is 24. The shift is (24 − 50) / 51 = −26/51 ≈ −0.5098. The new mean is 50 + (−0.5098) ≈ 49.49. So the mean decreases by about 0.51, moving to approximately 49.49. The standard deviation doesn’t affect the mean shift.

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