Question

(01.03 MC)

The Kelly school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table below, where Min represents the fewest days attended and Max represents the most days attended for a single student:

School
Min
Max
Range
Mean
Median
IQR
σ
High School M
128
180
52
141
160
55.5
41.5
High School N
131
180
49
159
154
48.5
36.5
High School P
140
180
40
153
165
32.5
31.5
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. (5 points)

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. (5 points) (10 points)

Answer 1

a: School W is has the most consistent attendance

b: School W has the highest average attendance

Explanation:

For a:

The most consistent school will be the school whose data has the smallest variance. *Consistent doesn't mean the best, it's just the least differing among it's own data. The variance tells us how spread out the data is, so the school with the smallest variance is the most consistent.

See photo 1 for the calculations of the variances of each school...

For b:

Take the mean for each school. Whichever has a higher value is the school with the highest average.

See photo 1 for the calculations if the means for each school. (the mean is used to calculate variance, so we will do this part first)