Question

The Harlowe school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.

School Low High Range Mean Median IQR σ
High School A 98 180 82 158 148 55.5 35.2
High School B 105 180 75 145 124 48.5 28.2
High School C 102 180 78 169 151 53.5 31.3

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.

Answer 1

Part A: Students from high school B is the most consistent, because their standard deviation (σ=28.2) is the smaller than that of A and C. Smaller standard deviation means less variations among the values, or more consistence.

Part B: High school A has the highest average attendance, because it has higher mean (82) than B and C. Mean is mathematically the same as average, total number of days attended by all students divided by the number of students.