Dr. Tanner randomly selects six students each from three grades at his school. He asks each of the selected students about the number of hours per week they spend on extracurricular activities. He lists the data as shown.
Grade 6: 6,7,6,7,7,6
Grade 7:9,10,9,9,10,9
Grade 8:7,6,6,6,7,6
Dr. Tanner wants to use the data to estimate the median number of hours per week that students spend on extracurricular activities.
Which sample medians would be a better estimate of the median for all students at his school, and why?
To estimate the median for all students at his school, Dr. Tanner should calculate the median for each grade separately and then find the median of those three medians.
The median for Grade 6 is 6.5, the median for Grade 7 is 9, and the median for Grade 8 is 6.5.
Since the medians for Grade 6 and Grade 8 are the same at 6.5, it is better to use these two medians as they represent a wider range of values compared to Grade 7's median of 9. By using the medians of Grade 6 and Grade 8, Dr. Tanner will have a better estimate of the median number of hours per week that students spend on extracurricular activities at his school.