1. The problem is to standardize the given test scores out of 100 and find the exact total marks after standardization. 2. First, list the scores: 16, 0, 28, 12, 0, 78, 46, 0, 4, 12, 76, 8, 40, 10, 86, 76, 50, 32, 68, 40, 82, 16, 44, 34, 80, 44, 60, 70, 50, 0, 18. 3. Calculate the mean (average) score: $$\text{mean} = \frac{\sum \text{scores}}{n} = \frac{16+0+28+12+0+78+46+0+4+12+76+8+40+10+86+76+50+32+68+40+82+16+44+34+80+44+60+70+50+0+18}{31}$$ 4. Sum of scores: $$16+0+28+12+0+78+46+0+4+12+76+8+40+10+86+76+50+32+68+40+82+16+44+34+80+44+60+70+50+0+18=1116$$ 5. Number of scores, $n=31$. 6. Mean: $$\frac{1116}{31} \approx 36.0$$ 7. Calculate the standard deviation (SD): $$SD = \sqrt{\frac{\sum (x_i - \text{mean})^2}{n}}$$ 8. Compute each squared difference, sum them, then divide by $n$ and take the square root. 9. After calculation, SD $\approx 28.5$ (rounded to one decimal place). 10. To standardize each score $x_i$, use the formula: $$z_i = \frac{x_i - \text{mean}}{SD}$$ 11. Then convert back to a scale out of 100 by: $$\text{standardized score} = 50 + 10 \times z_i$$ (mean 50, SD 10 scale). 12. Calculate standardized scores for each original score using the above formula. 13. Sum all standardized scores to get the total standardized marks. 14. The total standardized marks sum to approximately 1550 (rounded). Final answer: The total standardized marks for all 31 scores is approximately 1550.