


Can someone help me understand the explanation underlying the 60% figure? I can''t figure out how they got this from the answer key. My understanding is
What are the median and the third quintile of the following data points, respectively?
9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%
A)
13.1%; 13.7%.
B)
13.1%; 13.6%.
C)
12.8%; 13.6%.
Explanation
The median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7th term.
The formula for determining quantiles is: Ly = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8th and 9th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 – 0.136) = 0.1372, or 13.7%.
Comments
Quintiles divide data into 5 equal parts, i.e. fifths. So 3rd quintile splits the data set into the lower 60% of values and the upper 40% of values. That's where 60 comes from.