STATISTICS :FREQUENCY DISTRIBUTIONS AND GRAPHS
COMPREHENSIVE COURSE NOTES STUDY GUIDE WITH
HIGH-YIELD REVISION NOTES, WORKED EXAMPLES,
PRACTICE QUESTIONS, DETAILED ANSWER
EXPLANATIONS, TABLE CONSTRUCTION METHODS,
HISTOGRAMS, FREQUENCY POLYGONS, OGIVES,
GRAPHICAL DATA PRESENTATION TECHNIQUES, AND
COMPLETE STATISTICS EXAM SUCCESS TOOLKIT |
UPDATED FOR 2026/2027 | LATEST EDITION
2-1 Organizing Data
Data collected in original form is called raw data. For example:
Raw Data: 2, 5, 8, 7, 2, 2, 6, 8, 5, 2, 5, 7, 4, 5, 6, 2, 8, 6
Frequency table from raw data:
Score f
8 3
7 2
6 3
5 4
, 4 1
2 5
• Each raw data value is placed into a quantitative or qualitative
category called a class.
• A class then is the number of data values contained in a specific
class called frequency.
Frequency Distribution
A frequency distribution is the organization of raw data in table form, using
classes and frequencies.
Two types of frequency distribution:
Type Description
Categorical Frequency Used for data that can be placed in specific
Distributions categories (nominal or ordinal level data).
Grouped Frequency When the range of the data is large, data is
Distributions grouped into classes that are more than one
unit in width.
Categorical Frequency Distributions
,Example: Twenty-five army inductees were given a blood test to determine
their blood type.
Formula: % = f/n × 100
Class Tally Frequency (f) Percent %
A IIII 5 5/25×100 = 20
B IIII II 7 7/25×100 = 28
O IIII IIII 9 9/25×100 = 36
AB IIII 4 4/25×100 = 16
Total n = 25
Grouped Frequency Distributions
Class limits and class boundaries:
• Lower class limit: the smallest data value that can be included in the
class.
• Upper class limit: the largest data value that can be included in the
class.
• Class boundaries: used to separate classes so there is no gap in the
frequency distribution.
• Lower boundary = lower limit − 0.5
• Upper boundary = upper limit + 0.5
, Class Limits Class Tally Frequency
Boundaries
24–30 23.5–30.5 /// 3
31–37 30.5–37.5 / 1
38–44 37.5–44.5 //// 5
45–51 44.5–51.5 //// //// 9
52–58 51.5–58.5 //// / 6
59–65 58.5–65.5 / 1
Note on decimal places:
Class limits should have the same decimal place value as the data, but the
class boundaries should have one additional place value and end in a 5.
Example: Class limit 7.8–8.8 → Class boundary 7.75–8.85
• Lower boundary = 7.8 − 0.05 = 7.75
• Upper boundary = 8.8 + 0.05 = 8.85
Questions — Find Class Boundaries
Find the class boundaries for each class:
• 2.15 – 3.93
• 49.005
The numbers used to separate the classes so that there are no gaps in the
frequency distribution are called class boundaries.
COMPREHENSIVE COURSE NOTES STUDY GUIDE WITH
HIGH-YIELD REVISION NOTES, WORKED EXAMPLES,
PRACTICE QUESTIONS, DETAILED ANSWER
EXPLANATIONS, TABLE CONSTRUCTION METHODS,
HISTOGRAMS, FREQUENCY POLYGONS, OGIVES,
GRAPHICAL DATA PRESENTATION TECHNIQUES, AND
COMPLETE STATISTICS EXAM SUCCESS TOOLKIT |
UPDATED FOR 2026/2027 | LATEST EDITION
2-1 Organizing Data
Data collected in original form is called raw data. For example:
Raw Data: 2, 5, 8, 7, 2, 2, 6, 8, 5, 2, 5, 7, 4, 5, 6, 2, 8, 6
Frequency table from raw data:
Score f
8 3
7 2
6 3
5 4
, 4 1
2 5
• Each raw data value is placed into a quantitative or qualitative
category called a class.
• A class then is the number of data values contained in a specific
class called frequency.
Frequency Distribution
A frequency distribution is the organization of raw data in table form, using
classes and frequencies.
Two types of frequency distribution:
Type Description
Categorical Frequency Used for data that can be placed in specific
Distributions categories (nominal or ordinal level data).
Grouped Frequency When the range of the data is large, data is
Distributions grouped into classes that are more than one
unit in width.
Categorical Frequency Distributions
,Example: Twenty-five army inductees were given a blood test to determine
their blood type.
Formula: % = f/n × 100
Class Tally Frequency (f) Percent %
A IIII 5 5/25×100 = 20
B IIII II 7 7/25×100 = 28
O IIII IIII 9 9/25×100 = 36
AB IIII 4 4/25×100 = 16
Total n = 25
Grouped Frequency Distributions
Class limits and class boundaries:
• Lower class limit: the smallest data value that can be included in the
class.
• Upper class limit: the largest data value that can be included in the
class.
• Class boundaries: used to separate classes so there is no gap in the
frequency distribution.
• Lower boundary = lower limit − 0.5
• Upper boundary = upper limit + 0.5
, Class Limits Class Tally Frequency
Boundaries
24–30 23.5–30.5 /// 3
31–37 30.5–37.5 / 1
38–44 37.5–44.5 //// 5
45–51 44.5–51.5 //// //// 9
52–58 51.5–58.5 //// / 6
59–65 58.5–65.5 / 1
Note on decimal places:
Class limits should have the same decimal place value as the data, but the
class boundaries should have one additional place value and end in a 5.
Example: Class limit 7.8–8.8 → Class boundary 7.75–8.85
• Lower boundary = 7.8 − 0.05 = 7.75
• Upper boundary = 8.8 + 0.05 = 8.85
Questions — Find Class Boundaries
Find the class boundaries for each class:
• 2.15 – 3.93
• 49.005
The numbers used to separate the classes so that there are no gaps in the
frequency distribution are called class boundaries.
