To determine which graph has the least standard deviation among the scores of students $P, Q, R, S, T, U$, we need to find the graph where the scores are most consistent (closer to the mean).

Steps to Analyze the Graphs

1. Standard deviation measures how spread out the values are from the mean. A smaller spread leads to a lower standard deviation.
2. Look at the graphs:
   • If the heights of the bars (scores) are close to each other, the standard deviation will be smaller.
   • If there are bars with extreme heights (higher variability), the standard deviation will be larger.

Observing the Graphs

1. Exam 1: The scores for all students seem to be close together, mostly within the range of 70–80.
2. Exam 4: There is significant variability. Some scores are at 70, while others are at 100.
3. Exam 3: The scores are widely spread, with a mix of very high (100) and low (70) scores.
4. Exam 2: Similar to Exam 3, there is visible variability, with some bars higher (close to 100) and others lower (70).

Conclusion

The Exam 1 graph has the least standard deviation because the scores are the most consistent, all clustered closely between 70 and 80.

Let me know if you need further clarification or a detailed explanation of standard deviation.

Related Questions:

1. What is the formula for standard deviation, and how is it calculated?
2. Why is standard deviation a better measure of spread than range?
3. How would the mean and median scores compare for each exam?
4. What happens to standard deviation if all scores increase by the same amount?
5. Can you calculate the actual standard deviation for any of these exams?

Tip:

When analyzing variability in data, always focus on how close the values are to the mean. Smaller variability means less spread and a lower standard deviation.