**Answer:**

**High School P has the most consistent attendance among its students. **

**School N should be awarded for the highest average attendance.**

**Step-by-step explanation:**

Consider the provided information.

Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically.

**Standard deviation (σ) is a measure of how a data set is spread out.**

**If the standard deviation is low, this implies that the information tends to be near to the set mean, whereas a high standard deviation implies that the information points are spread across a wider spectrum of values.**

Therefore, for more consistency we need to look for the low standard deviation.

From the provided table we can see that the school P has low standard deviation (σ) i.e 31.5

**Hence, High School P has the most consistent attendance among its students.**

Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically.

**The formula for mean is:**

Mean is the same as average.

The sum of mean or average will be larger if each students contributes more attendance.

For highest average attendance the school with higher mean should be awarded.

**Hence, School N should be awarded for the highest average attendance.**