Step-by-step Solution:

Let the two observations be \( a \) and \( b \). Step 1: Given Information - Arithmetic Mean (AM): \[ \frac{a + b}{2} = 125 \] \[ a + b = 250 \] - Geometric Mean (GM): \[ \sqrt{a b} = 60 \] \[ ab = 3600 \] Step 2: Finding Harmonic Mean (HM) The formula for Harmonic Mean (HM) is: \[ HM = \frac{2ab}{a + b} \] Substituting the values: \[ HM = \frac{2 \times 3600}{250} \] \[ HM = \frac{7200}{250} = 28.8 \] Thus, the harmonic mean is: \[ \boxed{28.8} \]