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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 1.43Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
00.775.25.74)8)(3125(.5.74)2735(16
55.7450
P
Determine (compute) the 50th Percentile (P50) for the statistics exam scores.
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 1.43Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
64.661429.25.64)3)(7143(.5.64)1114(7
55.6420
P
Determine (compute) the 20th Percentile (P20) for the statistics exam scores.
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 1.43Note. The Relative fs were removed from this table since they are not required to calculate percentiles and/or percentile ranks.
25.8475.45.79)5.9)(5(.5.79)435.52(10
55.7975
P
Determine (compute) the 75th Percentile (P75) for the statistics exam scores.
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 1.43Note. 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.
71.781007871.70
1.55100
70
1.253100
70
)5.1)(4.1(53100
70
)5.8486(57
53
86
PR
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 1.43Note. 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.
43.91000943.70
6.6100
70
6.33100
70
)5.4)(8(.3100
70
)5.5459(54
3
59
PR
Graphing DataConstructing a Graph
Y axis
X axis
Origin = 0Independent Variable
Dependent Variable(Frequencies)
ThreeThree--QuarterQuarter--High RuleHigh RuleThe height of the Y axis shouldbe approximately three-quarters
the length of the X axis.
Y axis
X axis
Origin = 0Independent Variable
Dependent Variable(Frequencies)
ThreeThree--QuarterQuarter--High RuleHigh RuleThe height of the Y axis shouldbe approximately three-quarters
the length of the X axis.
Good Housekeeping seal
YesNo
Mean P
refe
rence
15
14
13
12
11
10
9
8
7
6
5
4
3
2
10
Good Housekeeping seal
YesNo
Mean P
refe
rence
14
13
12
11
10
Distorting Data Through Graphing…
Distorting Data Through Graphing…
Frequency distributions of nominal or ordinal (categorical) dataare customarily plotted using the bar graph.
Frequency distributions of interval or ratio (continuous) data
are customarily plotted using the histogram.
SHAPES of Frequency Curves
Stem Leaf
3 0 1 2 5 6 6 9 9
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
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