Raw Scores
Un-Grouped Frequency Distribution
Grouped Frequency Distribution
Percentile and Percentile Rank
• Percentile (PX) or Percentile Point
– The value on the measurement scale (at or) below
which a specified percentage of the scores in the
distribution fall.
– Where x from Px is a percentage
– Looking for a score (value)
• Percentile Rank (PRX)
– The percentage of scores with values (equal or)
lower than the score in question.
– Where x from PRx is a score (value)
– Looking for a percentage
Table 3.7 (p. 46)
Relative frequency, cumulative frequency, and cumulative percentage distributions…
Class Interval
Real Limits
f
Cumulative f
Cumulative %
95 – 99
94.5 – 99.5
4
70
100.00
90 – 94
89.5 – 94.5
6
66
94.29
85 – 89
84.5 – 89.5
7
60
85.71
80 – 84
79.5 – 84.5
10
53
75.71
75 – 79
74.5 – 79.5
16
43
61.43
70 – 74
69.5 – 74.5
9
27
38.57
65 – 69
64.5 – 69.5
7
18
25.71
60 – 64
59.5 – 64.5
4
11
15.71
55 – 59
54.5 – 59.5
4
7
10.00
50 – 54
49.5 – 54.5
2
3
4.29
45 – 49
44.5 – 49.5
1
1
1.43
Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
Determine (compute) the 50th Percentile (P50) for the statistics exam scores.
 5 
P50  74 . 5  
 ( 35  27 )  74 . 5  (. 3125 )( 8 )  74 . 5  2 . 5  77 . 00
 16 
Table 3.7 (p. 46)
Relative frequency, cumulative frequency, and cumulative percentage distributions…
Class Interval
Real Limits
f
Cumulative f
Cumulative %
95 – 99
94.5 – 99.5
4
70
100.00
90 – 94
89.5 – 94.5
6
66
94.29
85 – 89
84.5 – 89.5
7
60
85.71
80 – 84
79.5 – 84.5
10
53
75.71
75 – 79
74.5 – 79.5
16
43
61.43
70 – 74
69.5 – 74.5
9
27
38.57
65 – 69
64.5 – 69.5
7
18
25.71
60 – 64
59.5 – 64.5
4
11
15.71
55 – 59
54.5 – 59.5
4
7
10.00
50 – 54
49.5 – 54.5
2
3
4.29
45 – 49
44.5 – 49.5
1
1
1.43
Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
Determine (compute) the 20th Percentile (P20) for the statistics exam scores.
5
P20  64 . 5    (14  11 )  64 . 5  (. 7143 )( 3 )  64 . 5  2 . 1429  66 . 64
7
Table 3.7 (p. 46)
Relative frequency, cumulative frequency, and cumulative percentage distributions…
Class Interval
Real Limits
f
Cumulative f
Cumulative %
95 – 99
94.5 – 99.5
4
70
100.00
90 – 94
89.5 – 94.5
6
66
94.29
85 – 89
84.5 – 89.5
7
60
85.71
80 – 84
79.5 – 84.5
10
53
75.71
75 – 79
74.5 – 79.5
16
43
61.43
70 – 74
69.5 – 74.5
9
27
38.57
65 – 69
64.5 – 69.5
7
18
25.71
60 – 64
59.5 – 64.5
4
11
15.71
55 – 59
54.5 – 59.5
4
7
10.00
50 – 54
49.5 – 54.5
2
3
4.29
45 – 49
44.5 – 49.5
1
1
1.43
Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
Determine (compute) the 75th Percentile (P75) for the statistics exam scores.
 5 
P75  79 . 5  
 ( 52 . 5  43 )  79 . 5  (. 5 )( 9 . 5 )  79 . 5  4 . 75  84 . 25
 10 
Table 3.7 (p. 46)
Relative frequency, cumulative frequency, and cumulative percentage distributions…
Class Interval
Real Limits
f
Cumulative f
Cumulative %
95 – 99
94.5 – 99.5
4
70
100.00
90 – 94
89.5 – 94.5
6
66
94.29
85 – 89
84.5 – 89.5
7
60
85.71
80 – 84
79.5 – 84.5
10
53
75.71
75 – 79
74.5 – 79.5
16
43
61.43
70 – 74
69.5 – 74.5
9
27
38.57
65 – 69
64.5 – 69.5
7
18
25.71
60 – 64
59.5 – 64.5
4
11
15.71
55 – 59
54.5 – 59.5
4
7
10.00
50 – 54
49.5 – 54.5
2
3
4.29
45 – 49
44.5 – 49.5
1
1
1.43
Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
Determine (compute) the percentile rank (PR) for a score of 86.
PR 86 
7
53  
5

 ( 86  84 . 5 )
53  (1 . 4 )( 1 . 5 )
53  2 . 1
55 . 1

 100 
 100 
 100 
 . 7871  100  78 . 71
70
70
70
70
Table 3.7 (p. 46)
Relative frequency, cumulative frequency, and cumulative percentage distributions…
Class Interval
Real Limits
f
Cumulative f
Cumulative %
95 – 99
94.5 – 99.5
4
70
100.00
90 – 94
89.5 – 94.5
6
66
94.29
85 – 89
84.5 – 89.5
7
60
85.71
80 – 84
79.5 – 84.5
10
53
75.71
75 – 79
74.5 – 79.5
16
43
61.43
70 – 74
69.5 – 74.5
9
27
38.57
65 – 69
64.5 – 69.5
7
18
25.71
60 – 64
59.5 – 64.5
4
11
15.71
55 – 59
54.5 – 59.5
4
7
10.00
50 – 54
49.5 – 54.5
2
3
4.29
45 – 49
44.5 – 49.5
1
1
1.43
Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
Determine (compute) the percentile rank (PR) for a score of 59.
PR 59
4
3    ( 59  54 . 5 )
3  (. 8 )( 4 . 5 )
3  3 .6
6 .6
5

 100 
 100 
 100 
 . 0943  100  9 . 43
70
70
70
70
Graphing Data
Constructing a Graph
Y a x is
T h re e - Q u a rte r - H ig h R u le
T h e h e ig h t o f th e Y a x is s h o u ld
b e a p p ro x im a te ly th re e -q u a rte rs
th e le n g th o f th e X a x is .
D e p e n d e n t V a ria b le
(F re q u e n c ie s )
X a x is
In d e p e n d e n t V a ria b le
O rig in = 0
Distorting Data Through Graphing…
14
15
14
13
12
13
11
10
9
8
12
7
M ean P referenc e
6
11
10
No
Good Housekeeping seal
Y es
5
4
3
2
1
0
No
Good Housekeeping seal
Y es
Distorting Data Through Graphing…
Frequency distributions of nominal or ordinal (categorical) data
are customarily plotted using the bar graph.
Frequency distributions of interval or ratio (continuous) data
are customarily plotted using the histogram.
SHAPES of Frequency Curves
Given the following set of scores, determine the stem and leaf for the 30s:
10 31 25 35 30 39 45 36 36 68 39 32
Stem Leaf
3 0 1 2 5 6 6 9 9