Frequency, Percentage, and
Proportion
Statistical Symbols
• X or x = Individual Subject/value/score
• N or n = Total number of
subjects/values/scores
Frequency Distributions
• an organization of raw data into tabular forms
using categories/intervals and frequencies
– frequency/frequency count
• the # of times a specific value occurs in the data set
– often represented by the symbol f
• 3 main types
– categorical, ungrouped, & grouped
Frequency Distributions
• Categorical
– AKA Qualitative Frequency Distribution
• represents data that can be placed in specific
categories
– Gender, Hair Color, Religious Affiliation
• Ex:
AB
B
A
O
B
O
B
O
A
O
B
O
B
B
B
A
O
AB
AB
O
A
B
AB
O
A
Frequency Distributions
• Ex: Categorical Frequency Table
Category:
Blood Type
Frequency f
A
5
B
8
O
8
AB
4
Total
25
Frequency Distributions
• Ungrouped
– a simple listing of the data values w/ the f w/ which each
value occurs.
• Ex:
Day
1
2
3
4
5
6
7
8
9
10
Defects
10
10
6
12
6
9
16
20
11
10
Day
11
12
13
14
15
16
17
18
19
20
Defects
11
11
9
12
11
7
10
11
14
21
Day
21
22
23
24
25
Defects
12
6
10
11
6
Frequency Distributions
• Ex: Ungrouped Frequency Table
Frequency Distributions
• Often times, the researcher will also display
the relative frequency and the corresponding
percentages
– relative frequency for any value (class)
• obtained by dividing the f for that class by the total
number of observations
Frequency Distributions
• Ex: Ungrouped Frequency Table w/ Relative
Frequency and Percentage
Frequency Distributions
• Sometimes, the researcher will also display
the cumulative frequencies and the
cumulative relative frequencies
– cumulative frequencies
• for any specific value, the sum of the f for all values at
or below the given value
– cumulative relative frequencies
• for any specific value, the sum of the relative
frequencies for all values at or below the given value
Frequency Distributions
• Ex: Ungrouped Frequency Table w/ Cumulative
Frequency and Cumulative Relative Frequency
Frequency Distributions
• Grouped
– obtained by constructing intervals of the values
for the data and then listing the corresponding f
in each interval.
• Ex:
Frequency Distributions
• Ex: Ungrouped Frequency Table w/ Cumulative
Frequency and Cumulative Relative Frequency