Class Practice on Percentiles and Quartiles #2
Consider the following scores on a practice test.
15
18
18
19
20
21
21
21
22
23
24
25
26
29
35
36
36
38
39
40
Find the 30th percentile.
First we calculate
nk 20 • 30
=
=6
100
100
Since 6 is an integer we rewrite it as 6.5 according to the procedure outlined on
the Class Practice on Percentiles and Quartiles #1.
Next we go to the 6.5th position in the ranked data.
So, P30 = 21.
We can check our answer. There should be (at most) 30% of the data in the
data set that is less than 21. Looking at the data, we see 5 out of 20 numbers
that are less than 21. 5 out of 20 is 5/20 = 25% which is less than 30%.
(Looks correct.)
Consider the same scores.
15
18
18
19
20
21
21
21
22
23
24
25
26
29
35
36
36
38
39
40
Find the 60th percentile.
First we calculate
nk 20 • 60
=
= 12
100
100
Since 12 is an integer we rewrite it as 12.5 according to the procedure outlined
on the Class Practice on Percentiles and Quartiles #1.
Next we go to the 12.5th position in the ranked data.
So, P60 = 25.5.
We can check our answer. There should be (at most) 60% of the data in the
data set that is less than 25.5. Looking at the data, we see 12 out of 20
numbers that are less than 25.5. 12 out of 20 is 12/20 = 60% which is exactly
equal to 60%. (Looks correct.)
Consider the same scores.
15
18
18
19
20
21
21
21
22
23
24
25
26
29
35
36
36
38
39
40
Find the 83rd percentile.
First we calculate
nk 20 • 83
=
= 16.6
100
100
Since 16.6 is not an integer we rewrite it as 17 according to the procedure
outlined on the Class Practice on Percentiles and Quartiles #1.
Next we go to the 17th position in the ranked data.
So, P83 = 36.
We can check our answer. There should be (at most) 83% of the data in the
data set that is less than 36. Looking at the data, we see 15 out of 20 numbers
that are less than 36. 15 out of 20 is 15/20 = 75% which is less than 83%.
(Looks correct.)
Consider the same scores.
15
18
18
19
20
21
21
21
22
23
24
25
26
29
35
36
36
38
39
40
Find the 86th percentile.
First we calculate
nk 20 • 86
=
= 17.2
100
100
Since 17.2 is not an integer we rewrite it as 18 according to the procedure
outlined on the Class Practice on Percentiles and Quartiles #1.
Next we go to the 18th position in the ranked data.
So, P86 = 38.
We can check our answer. There should be (at most) 86% of the data in the
data set that is less than 38. Looking at the data, we see 17 out of 20 numbers
that are less than 38. 17 out of 20 is 17/20 = 85% which is less than 86%.
(Looks correct.)