The document outlines the concept of frequency distribution, which describes how often each value occurs in a data set. It details various types of frequency distributions, including ungrouped, grouped, relative, and cumulative distributions, along with examples of how to create tables for each type. Additionally, it provides instructions for analyzing data and interpreting frequency distributions for both categorical and quantitative variables.

1. Distribution
Frequency

2. The frequency is how often a
value occurs in an interval, while
distribution is the pattern of
frequency of the variable.
What is Frequency Distribution?

3. A frequency distribution is the
pattern of frequencies of a
variable. It’s number of times
each possible value of a
variable occurs in a data set.

4. A frequency distribution are
depicted using graphs and
frequency tables.

5. Types of Frequency
Distribution
1.Ungrouped
2. Grouped
3. Relative
4. Cumulative

6. 1. Ungrouped Frequency
Distribution
is a type of frequency
distribution that displays the
frequency of each individual data
value instead of groups of data
values. We can directly see how
often different values occurred in
the table.

7. You can use this type of frequency
distribution for categorical
variables.

8. 1. Create a table with 2 columns. First
column is for the “name” of label and the
second column is for “frequency.”
 For ordinal variables, the values should be
ordered from smallest-largest in the table
rows.
How to make an ungrouped
frequency table?

9. 2. Count the frequencies. The frequencies are
the number of times each value occurs.
 Especially if your dataset is large, it may
help to count the frequencies by tallying.
Add third column called “tally. ”

10. Example #1:
A gardener set up a bird feeder in
their backyard. To help them decide
how much and what type of birdseed
to buy, they decide to record bird
species that visit their feeder. Over the
course of one morning, the following
birds visit their feeder.

11. Bird Species Tally Marks Frequency
Chickadee III 3
Dove I 1
Finch IIII 4
Grackie II 2
Sparrow IIII 4
Starling II 2

12. Example #2:
4 families had 1 pet
3 families had 2 pets
2 families had 3 pets
1 family had 4 pets

13. Solution:
Number of Pets Frequency
1 4
2 3
3 2
4 1

14. Take note that ungrouped
frequency distributions work
best with small datasets in
which there are only a few
unique values.

15. 2. Grouped Frequency Distribution
The number of observations of each
class interval of a variable. Class
intervals are ordered groupings of a
variable’s values. You can use this type of
frequency distribution for quantitative
variables.

16. How to make a grouped frequency
table?
1. Divide the variable into class intervals.
• Calculate the range. Subtract the lowest value in
the dataset from the highest.
• Decide the class interval width. There are no firm
rules on how to choose the width but the
following formula is a rule of thumb.

17. width
• You can round this value to a whole number or a
number that’s convenient to add (such as a multiple of
10)
• Calculate the class intervals. Each interval is defined by
a lower limit and upper limit. Observation in a class
interval are greater than or equal to the lower limit
and less than the upper limit:

18. • The lower limit of the first interval is the
lowest value in the dataset. Add the
class interval width to find the upper
limit of the first interval and the lower
limit of the second variable. Keep
adding the interval width to calculate
more class intervals until you exceed
the highest value.

19. 2. Create a table with two columns and as
many rows as there are class intervals.
Label the first column using the variable
“name” and label the second column
“frequency.” Enter the class intervals in the
first column.
3. Count the frequencies. The frequencies
are the number of observations in each

20. Example :
A sociologist conducted a survey of 20
adults. She wants to report the frequency
distribution of ages of the survey
respondents. The respondents were the
following ages in years.
52, 34, 32, 29, 63, 40, 46, 54, 36, 36, 24, 19,
45, 20, 28, 29, 38, 33, 49, 37

21. Range= highest – lowest
Range= 63-19
Range= 44
width
width
Width= 9.84

22. Example #2:

24. 3. Relative Frequency Distributions
The proportion of observations of each
value or class interval of a variable. You can
use this type of frequency distribution for any
type of variable when you’re more interested
in comparing frequencies than the actual
number of observations.

25. How to make a relative frequency table?
1. Create an ungrouped or grouped
frequency table.
2. Add a third column to the table for the
relative frequencies. To calculate the relative
frequencies, divide each frequency by the
sample size. The sample size is the sum of the
frequencies.

26. Relative Frequency Formula
Relative frequency
Or Relative frequency
where,
 f is the number of times the data occurred in an
observation
 N= total frequency

27. Example :

28. From this table, the gardener can make
observations, such as that 19% of the
bird feeder visits were from chikadees
and 25% were from finches and sparrow.

29. The sum of the frequencies less than or
equal to each value or class interval of a
variable. You can use this type of
frequency distribution for ordinal or
quantitative variables when you want to
understand how often observations fall
below certain values.
4. Cumulative Frequency Distributions

30. 1. Create an ungrouped or grouped frequency table for an ordinal or
quantitative variable. Cumulative frequencies don’t make sense for
nominal variables because the values have no order, one value isn’t
more than or less than another value.
2. Add a third column to the table for the cumulative frequencies. The
cumulative frequency is the number of observations less than or equal
to a certain value or class interval.
How to make a cumulative frequency
table?

31. To calculate the relative frequencies, add each frequency to
the frequencies in the previous rows.
3. Optional: If you want to calculate the cumulative relative
frequency, add another column and divide each cumulative
frequency by the sample size.

32. Example:

33. From this table, the sociologist can make
observations such as 13 respondents
(65%) were under 39 years old, and 16
respondents (80%) were under 49 years
old.

34. A. Direction: Answer the following
question by filling the blank with the
correct answer. Choose your answer in the
box below.
Activities:
Frequency
Distribution
Ungrouped
Frequency
Distribution
Grouped
Frequency
Distribution
Relative
Frequency
Distribution
Cumulative
Frequency
Distribution

35. ______1. This type of frequency
distribution can be used for categorical
variables.
______2. You can use this type of
frequency distribution for any type of
variable such as comparing frequencies
than the actual number of observations.

36. ______3. It describes the number of
observations for each possible value of a
variable using graphs and frequency
tables.
______4. This type of frequency
distribution refers to the sum of
frequencies less than or equal to each
value or class interval of a variable.

37. ______5. Another type of frequency
distribution that can be used for
quantitative variables.

38. B. Analyze and answer the following
problems using ungrouped, grouped,
relative and cumulative frequency
distribution.
1. The marks obtained by the Grade 2
pupils in Mathematics test are given as:
52, 46, 92, 78, 62, 44, 34, 46, 58, 52.
Prepare an ungrouped frequency table

39. 2. The ages of 30 people in your locality
is 5, 65, 62, 48, 5, 23, 17, 40, 30, 30, 30,
51, 5, 17, 17, 39, 23, 48, 40, 65, 65, 62, 5,
5, 17, 62, 51, 23, 48, 40.
The age ranges from 5 to 65.
3. Solve the problem below for the
relative frequency.

40. Name of Car Frequency Relative Frequency
Honda 7
Toyota 3
Hyundai 5
Mitsubishi 5
Suzuki 6
Ford 7
BMW 9

41. 4. A basketball coach had each player on
the team shoot ten free throws, and he
kept track of how many free throws each
player made. Find the cumulative
frequency of the free throws made by
each basketball player.

42. Free throws made Frequency Cumulative Frequency
3 1
5 1
8 2
2 4
6 2

43. Thank you!