1. **Problem Statement:** A researcher selected every 20th name from a list of 500 Grade 10 students. 2. **Identify the sampling method:** This is systematic sampling where every $k^{th}$ element is selected. 3. **Given data:** - Population size $N = 500$ - Sampling interval $k = 20$ 4. **Calculate sample size $n$:** $$n = \frac{N}{k} = \frac{500}{20} = 25$$ 5. **Random start:** The researcher should randomly select a starting point between 1 and $k$ (1 to 20) to begin sampling. 6. **Summary:** - Population size $N = 500$ - Sample size $n = 25$ - $k^{th}$ element = 20 - Random start = any number from 1 to 20 This ensures a systematic and unbiased sample from the population.