1. **Problem:** Given the standard scores (z-scores) for five values are 0.5, k, 0, -0.5, and 1.5, find the value of k. 2. **Formula and rule:** The sum of all standard scores (z-scores) for a data set is always zero because z-scores represent deviations from the mean in units of standard deviation. 3. **Set up the equation:** $$0.5 + k + 0 + (-0.5) + 1.5 = 0$$ 4. **Simplify the sum:** $$0.5 - 0.5 + 1.5 + k = 0$$ $$\cancel{0.5} - \cancel{0.5} + 1.5 + k = 0$$ $$1.5 + k = 0$$ 5. **Solve for k:** $$k = -1.5$$ **Final answer:** $$\boxed{-1.5}$$