1. **Problem statement:** Calculate the mean and standard deviation for a class of 50 students who all scored 16 marks out of 20 in an IT module. 2. **Mean calculation:** The mean is the average score, calculated by summing all scores and dividing by the number of students. Since all 50 students scored 16, the total sum of scores is $$50 \times 16 = 800$$. Mean $$\bar{x} = \frac{\text{Total sum of scores}}{\text{Number of students}} = \frac{800}{50} = 16$$. 3. **Standard deviation calculation:** Standard deviation measures the spread of scores around the mean. The formula for standard deviation $$\sigma$$ is: $$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \bar{x})^2}$$ where $$x_i$$ are individual scores, $$\bar{x}$$ is the mean, and $$N$$ is the number of students. 4. **Applying the formula:** Since all scores are equal to the mean (16), each $$x_i - \bar{x} = 0$$. Therefore, $$\sum (x_i - \bar{x})^2 = 0$$. Hence, $$\sigma = \sqrt{\frac{0}{50}} = 0$$. 5. **Interpretation:** The mean score is 16, and the standard deviation is 0, indicating no variation in scores; all students scored the same. **Final answers:** - Mean = 16 - Standard deviation = 0