3
.
Frequency Distributions
Grouped Data
Percentiles, Deciles & Quartiles
Graphical Representations
Symmetry and Skewness
STATISTICAL
DESCRIPTION
OF DATA

Statistical data collected should be
arranged in such a manner that
will allow a reader to distinguish
their essential features. Depending
on the type and the objectives of
the person presenting the
information, data may be
presented using one or a
combination of three forms.

Three Forms of Presenting
Data
Textual Form
– data is
presented in paragraph
form
especially
when
they
are
purely
qualitative or when very
few
numbers
are
involved.

Tabular Form
- data
is presented in
rows and columns
Graphical Form
- data
is presented in visual
form
0
500
1000
1500
2000
2500
3000
3500
4000
1991
1992
1993
1994
1995

When that data include a large
number of observations, it is
convenient to group the values into
mutually exclusive classes and show
the number of observations
occurring in each class in a tabular
form.

Frequency Distribution
A
frequency distribution
is the
arrangement of data that shows the
frequency of occurrence of values
falling
within
arbitrarily
defined
ranges of the variable known as
class intervals
. The smallest and
largest values that fall in a given
interval are called
class
limits
.

Class Frequency and Class
Mark
Class frequency
refers to the
number of observations falling in a
particular class while the midpoint
between the upper and lower class
limits is called
class
mark/midpoint
.

Steps in Making a Frequency
Distribution
Find the range.
Determine the interval size by dividing the
range by the desired number of classes
which is normally not less than 10 and not
more than 20.
Determine the class limits of the class
intervals. Tabulation is facilitated if the
lower class limits of the class intervals are
multiples of the class size. The bottom
interval must include the lowest score.

List the intervals, beginning at the
bottom.
Tally the frequencies.
Summarize these under a column
labeled f.
Total this column and record the
number at the bottom.

Proble
m:
Construct a frequency distribution
of the given scores on a test.
56
28
42
56
47
39
62
60
54
47
78
82
55
56
41
44
54
42
62
48
79
38
57
55
50
47
42
56
68
53
37
72
65
66
52
52
48
48
42
68

Solutio
n:
Computing for the range:
R =
82 – 28 = 54
Computing for the class interval:
Therefore, class interval
may be 5 or 6.
4
.
5
10
54
i

We choose
5
because it is the odd number.
If
i = 5
,
lowest limit should be
We choose
25
because
it is the
smallest multiple of the chosen
interval which is smaller than the
smallest value in the set.
If lowest limit is
25
, the bottom interval
should be
25.
29 – 25.
The interval
29 - 25
contains the lowest
score (
28
).

Classes
29 - 25
34 - 30
39 - 35
44 - 40
49 - 45
54 - 50
59 - 55
64 - 60
69 - 65
74 - 70
79 - 75
84 - 80
Tally
f
40
f
N
1
1
1
4
4
7
6
6
6
3
0
1
/
/
/
////
////
///////
//////
//////
//////
///
/

For Grouped Data ( >
30
values)
Methods
:
1. Midpoint Method
2. Short Method
MEASURES OF CENTRAL TENDENCY
MEA
N

Midpoint Method
After the
f
column, make another column
and enter the midpoint (
X
m
) of each class.

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- Fall '17
- Antonino Magallen