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 1st
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.