raw scores. un-grouped frequency distribution grouped frequency distribution
Post on 19-Dec-2015
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Raw Scores
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Un-Grouped Frequency Distribution
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Grouped Frequency Distribution
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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
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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.
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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.
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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.
![Page 9: Raw Scores. Un-Grouped Frequency Distribution Grouped Frequency Distribution](https://reader034.vdocument.in/reader034/viewer/2022042508/56649d385503460f94a122ec/html5/thumbnails/9.jpg)
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
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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
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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.
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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…
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Distorting Data Through Graphing…
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Frequency distributions of nominal or ordinal (categorical) dataare customarily plotted using the bar graph.
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Frequency distributions of interval or ratio (continuous) data
are customarily plotted using the histogram.
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SHAPES of Frequency Curves
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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