To compare the exam scores of the two groups, we will use the mean and standard deviation values provided. The mean gives an idea of the average score, while the standard deviation tells us how spread out the scores are from the mean.

Group 1:

• Mean: 35.3
• Standard deviation: 3.6

Group 2:

• Mean: 34.1
• Standard deviation: 0.5

1. Comparing the Means:

The mean exam score for Group 1 is 35.3, while for Group 2 it is 34.1. Since the mean score of Group 1 is higher by 1.2 points, on average, the examinees in Group 1 performed slightly better than those in Group 2.

2. Comparing the Standard Deviations:

The standard deviation of Group 1 is 3.6, while for Group 2 it is 0.5. A higher standard deviation indicates a larger spread of scores around the mean.

• Group 1: A higher standard deviation means that the exam scores are more spread out. Some examinees may have scored much higher or lower than the mean score.
• Group 2: A much lower standard deviation indicates that most scores are very close to the mean, meaning there is less variability in their performance.

Conclusion:

• Group 1: While they have a higher average score, their performance is more inconsistent, with some examinees scoring far from the mean.
• Group 2: Though they have a lower average score, the scores are much more consistent and closely grouped around the mean.

Would you like more details or have any questions about the comparison? Here are 5 relative questions for further exploration:

1. How would the distribution shapes affect your interpretation of the results?
2. What would happen if the groups were combined? How would you calculate the new mean and standard deviation?
3. How can we calculate the coefficient of variation for each group, and what does it tell us?
4. How would you test if the difference in means is statistically significant?
5. How does the difference in standard deviations affect the reliability of the test scores?

Tip: When comparing datasets, standard deviation helps you understand the consistency of performance, while the mean helps you compare overall outcomes.