Question

What is the upper quartile, Q3, of the following data set? 54, 53, 46, 60, 62, 70, 43, 67, 48, 65, 55, 38, 52, 56, 41

Answer 1

The original data set is 
{54, 53, 46, 60, 62, 70, 43, 67, 48, 65, 55, 38, 52, 56, 41}

Sort the data values from smallest to largest to get
{38, 41, 43, 46, 48, 52, 53, 54, 55, 56, 60, 62, 65, 67, 70} 

Now find the middle most value. This is the value in the 8th slot. The first 7 values are below the median. The 8th value is the median itself. The next 7 values are above the median. 

The value in the 8th slot is 54, so this is the median

Divide the sorted data set into two lists. I'll call them L and U 
L = {38, 41, 43, 46, 48, 52, 53}
U = {55, 56, 60, 62, 65, 67, 70}
they each have 7 items. The list L is the lower half of the sorted data and U is the upper half. The split happens at the original median (54).

Q3 will be equal to the median of the list U
The median of U = {55, 56, 60, 62, 65, 67, 70} is 62 since it's the middle most value. 

Therefore, Q3 = 62

Answer: 62