8/08/2014 The numbers below denote the horsepower of n = 38 vehicles.

65, 65, 68, 68, 69, 70, 71, 71, 75, 78, 80, 80, 85, 88, 90, 90, 95, 97, 97, 103, 105, 109, 110, 110, 115, 115, 115, 120, 125, 125, 129, 130, 133, 135, 138, 142, 150, 155
a) Find the 1
st and 3rd Quartiles. Interpret the 1st Quartile.
b
) Find the 68th and interpret it.
c) A vehicle with a horsepower of 103hp lie in what percentile? Interpret it.

Scroll down for the solution.

8/08/2014 Solution.
a) For Q1, 0.25·38 = 9.5 → 10th value => 78hp
Interpretation: A car with a horsepower of 78 corresponds to the 25th percentile which means that 25% of all [given] vehicles have a horsepower of 78hp
or less.
Q3 = 129hp
b
) 0.68·38 = 25.84 ~ 26th value → 115hp
Interpretation: A car with a horsepower of 115 corresponds to the 68th percentile which means that 68% of all [given] vehicles have a horsepower of 115hp
or less.
Do this yourselves! Find the 91st percentile.
c) P(X
< 103) = 20/38 = 52.63rd percentile
Interpretation: A car with a horsepower of 103 corresponds to the 52.63rd percentile which means that 52.63% of all [given] vehicles have a horsepower of 103hp
or less.