Frequency Distribution

1. Frequency
Distribution

2. Key Terms
• Any data that has not been transformed/analyzed.
Raw Scores
• Description of the pattern of set of numbers by displaying
the count/proportion for each value of a variable
Frequency Distribution
• visual depiction of data that shows how often each value
occurred, that is, how many scores were at each value
Frequency Table

3. Frequency Distribution
Table: How to Create
1
• Find the range of the dataset
2
• Calculate the class interval
3
• Figure out the range of scores at the bottom

4. Making a Frequency
Distribution: An
Example

5. 1) Find the range
 Highest: 62
 Lowest: 13
 Range = 62 – 13
 Range = 49

6. 2) Calculate the value of
i(Interval)
ⅈ =
𝑅
10
ⅈ =
49
10
ⅈ = 4.90 ~ 5

7. 3) Create the frequency
table
NOTE: The value of the lowest value must be
lower than the lowest value and is divisible by
the value of i

8. 3) Create the frequency
table
Class Intervals
60-64
55-59
50-54
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14

9. 3) Create the frequency
table
Class
Intervals
Frequency
60-64 I
55-59 III
50-54 IIII
45-49 IIIII
40-44 IIIII
35-39 II
30-34 IIIII
25-29 II
20-24
15-19 II
10-14 I

10. 3) Create the frequency
table
Class
Intervals
f rf
60-64 1 0.03
55-59 3 0.10
50-54 4 0.13
45-49 5 0.17
40-44 5 0.17
35-39 2 0.07
30-34 5 0.17
25-29 2 0.07
20-24 0 0.00
15-19 2 0.07
10-14 1 0.03
Relative Frequency (rf)
-the fraction of the entire sample that is made
up by the times that a score occurs
𝑟𝑓 =
𝑓
𝑁

11. 3) Create the frequency
table
Class
Intervals
f rf cf
60-64 1 0.03 30
55-59 3 0.10 29
50-54 4 0.13 26
45-49 5 0.17 22
40-44 5 0.17 17
35-39 2 0.07 15
30-34 5 0.17 10
25-29 2 0.07 5
20-24 0 0.00 3
15-19 2 0.07 3
10-14 1 0.03 1
Cumulative Frequency (cf)
-frequency of all scores at or below a
particular score

12. 3) Create the frequency
table
Class
Intervals
f rf cf Percentiles
60-64 1 0.03 30 100%
55-59 3 0.10 29 97%
50-54 4 0.13 26 88%
45-49 5 0.17 22 74%
40-44 5 0.17 17 57%
35-39 2 0.07 15 50%
30-34 5 0.17 10 33%
25-29 2 0.07 5 17%
20-24 0 0.00 3 10%
15-19 2 0.07 3 10%
10-14 1 0.03 1 3%
Percentiles
-percent of all scores in
the data that are at or
below the score
=
𝐶𝑓
𝑛
100

13. Interpolation
 The process of determining a specific
percentile of a single value or the specific
percentile of a single value not reported in
a frequency distribution table.
 Finding the values that are located between
two specified numbers.

14. Interpolation
1
• Find the width
2
• Locate the position of the intermediate value in the interval.
3
• Use the same fraction to determine the corresponding position on
the other scale.
4
• Use the distance from the top to determine the position on the
other scale.

15. Interpolation: Example
Class
Intervals
f rf cf Percentiles
60-64 1 0.03 30 100%
55-59 3 0.10 29 97%
50-54 4 0.13 26 88%
45-49 5 0.17 22 74%
40-44 5 0.17 17 57%
35-39 2 0.07 15 50%
30-34 5 0.17 10 33%
25-29 2 0.07 5 17%
20-24 0 0.00 3 10%
15-19 2 0.07 3 10%
10-14 1 0.03 1 3%

16. Interpolation: Example
Find the 40th
percentile
Class
Intervals
f rf cf Percentiles
60-64 1 0.03 30 100%
55-59 3 0.10 29 97%
50-54 4 0.13 26 88%
45-49 5 0.17 22 74%
40-44 5 0.17 17 57%
35-39 2 0.07 15 50%
30-34 5 0.17 10 33%
25-29 2 0.07 5 17%
20-24 0 0.00 3 10%
15-19 2 0.07 3 10%
10-14 1 0.03 1 3%

17. Interpolation: Example
Scores X Percentile
Top 39.5 50%
Med 40%?
Bottom 34.5 33%
Class
Intervals
f rf cf Percentiles
60-64 1 0.03 30 100%
55-59 3 0.10 29 97%
50-54 4 0.13 26 88%
45-49 5 0.17 22 74%
40-44 5 0.17 17 57%
35-39 2 0.07 15 50%
30-34 5 0.17 10 33%
25-29 2 0.07 5 17%
20-24 0 0.00 3 10%
15-19 2 0.07 3 10%
10-14 1 0.03 1 3%
It is helpful to put a table in
simplifying the process

18. Interpolation: Example
1) find the width
Width of Scores
= 39.5 – 34.5
= 5
Width of Percentiles
=50 – 33
= 17
Scores X Percentile
Top 39.5 50%
Med 40%?
Bottom 34.5 33%

19. Interpolation: Example
2) locate intermediate
value
3) find distance
The value of 40% is
located 10 points
from the top
=10 divided by 17
=0.59
=0.59 x 5
= 2.95
Scores X Percentile
Top 39.5 50%
Med 40%?
Bottom 34.5 33%

20. Interpolation: Example
4) determine the value
39.5 – 2.95
= 36.55
Scores X Percentile
Top 39.5 50%
Med 40%?
Bottom 34.5 33%

21. Interpolation: Example
4) determine the value
Scores X Percentile
Top 39.5 50%
Med 36.55 40%?
Bottom 34.5 33%

22. Visual Displays of Data
 Histogram
 Frequency Polygon
 Ogive
 Bar Graph
 Pareto Charts
 Time Series Graph
 Pie Chart

23. Histogram
 is a graph that
displays the data
by using
contiguous
vertical bars
(unless the
frequency of a
class is 0) of
various heights to
represent the
frequencies of the
classes.

24. Frequency Polygon
 is a graph that
displays the data
by using lines that
connect points
plotted for the
frequencies at the
midpoints of the
classes. The
frequencies are
represented by
the heights of the
points

25. Ogive
 is a graph that
represents the
cumulative
frequencies for
the classes in a
frequency
distribution.

26. Bar Graph
 represents the
data by using
vertical or
horizontal bars
whose heights or
lengths represent
the frequencies of
the data.

27. Pareto Chart
 used to represent a
frequency
distribution for a
categorical variable,
and the frequencies
are displayed by
the heights of
vertical bars, which
are arranged in
order from highest
to lowest.

28. Time Series Chart
 represents data
that occur over a
specific period of
time.

29. Pie
 is a circle that is
divided into
sections or wedges
according to the
percentage of
frequencies in each
category of the
distribution
 Find the
percentages
 multiply the
percentages to 360.

30. Stem and Leaf Plot
 a data plot that
uses part of the
data value as the
stem and part of
the data value as
the leaf to form
groups or classes.