GROUP-10-Frequency-Distribution-and-Graphical-Representation.pptx

Frequency Distribution and Their
Graphic Representation
(Chapter 10)

Discussants
ADRIAN D. VENTURA
PRINCIPAL 1
SAMPALOC ES
Gainza District
Division of Camarines Sur
JAY P. MIRAÑA
PRINCIPAL 1
PATAG ES
Libmanan District 1
GEMLIN C. MIRAÑA
TEACHER III
TARUM ES
Libmanan District 1

• Tabulation of scores, showing the number of
individuals occur at each class limit arranged
from high to low or from low to high
• Is applicable if the total number of cases (N)
is equal to 30 or more.
Frequency Distribution

• In general, a frequency distribution is any
arrangement of the data that shows the
frequency of occurrence of different values of the
variable or the frequency occurrence of values
falling within arbitrarily defined ranges of the of
the variable known as class intervals
Frequency Distribution

Scores Made by 35 college
students in Botany Test
•STEP 1. Find the range
RANGE is equal to highest score minus lowest score
R= HS-LS
R= 47-12
R = 35
28 40 12 22
20 18 23 28
34 39 33 37
30 21 31 30
14 25 36 27
32 25 29 25
47 42 45 28
22 37 28 16
25 31 25
STEP IN ARRANGING THE SCORES IN A FORM OF
FREQUENCY DISTRIBUTION

Scores Made by 35 college
students in Botany Test
•STEP 2. Find the Class Interval
Class interval is the difference between the upper and the lower limits of a step
of test scores in a grouped of frequency distribution.
• In finding for the class interval, we simply divide the range (R) by 10 or 20 in order that the size of
the class limit or class interval may not be less than 10 and not more than 20 provided that such
class will cover the total range of the observations.
• To illustrate:
Range = 35
35/10= 3.5
35/20= 1.75
• The class interval ranges from 1.75 to 3.5. Therefore, we choose 3 as our class interval where we
will obtain 13 classes.
• The ideal class limit is 12 to 15. Hence, 13 class limit is within the ideal class.
• In choosing the class interval, odd number is preferable.
28 40 12 22
20 18 23 28
34 39 33 37
30 21 31 30
14 25 36 27
32 25 29 25
47 42 45 28
22 37 28 16
25 31 25

•STEP 3. Set up the Classes
• In setting up the classes, we add C/2 where C is the class interval to the highest score as the
upper limit of the highest class and subtract C/2 to the highest score as the lower limit of the
highest class.
47+(C/2) = upper limit of the highest class
47+ 1.5 = 48.5
47 – (C/2) = lower limit of the highest class
47 – 1.5 = 45.5
• The highest class limit is from 45.5 to 48.5.
• This setting of class is called the real limit or exact limit and these are sometimes spoken of
as class boundaries.
• Once the highest class is set, subtract 3 as your class interval to the next class until you reach
the lowest score.
Class Limit
Real Limits
45.5 – 48.5
42.5 – 45.5
39.5 – 42.5
36.5 – 39.5
33.5 – 36.5
30.5 – 33.5
27.5 – 30.5
24.5 – 27.5
21.5 – 24.5
18.5 – 21.5
15.5 – 18.5
12.5 – 15.5
9.5 – 12.5

•STEP 3. Set up the Classes
• There are 2 ways of setting up classes, namely, real limits
and integral limits.
• Integral limits is obtained by adding 0.5 to the lower
limit or a class interval and subtracting 0.5 to the upper
limit. For instance, the upper class is 45.5 to 48.5 for real
limits and 46 to 48 for integral limits.
Class Limit
Real Limits Integral Limits
45.5 – 48.5
42.5 – 45.5
39.5 – 42.5
36.5 – 39.5
33.5 – 36.5
30.5 – 33.5
27.5 – 30.5
24.5 – 27.5
21.5 – 24.5
18.5 – 21.5
15.5 – 18.5
12.5 – 15.5
9.5 – 12.5
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12

•STEP 4. Tally the Scores
• Having adopted a set of classes, we are ready to
tally them. Taking each score as it comes, locate it
within the proper class and tally. After tallying,
count the number of tallies in each class and write it
in column frequency (f). The frequencies are listed
in column 4.
• The tally should be carefully checked if the sum is
equal to the total number of scores in the sample. If
there is an unequal frequency from the sample,
tallying should be repeated. At the bottom of
column 4 the symbol N or ∑f in which ∑ (capital
Greek sigma) stands for the “sum of” equals 35 of
the total number of cases (N).
Classes
Real Limits Integral
Limits
Tally Frequency
45.5 –
48.5
42.5 –
45.5
39.5 –
42.5
36.5 –
39.5
33.5 –
36.5
30.5 –
33.5
27.5 –
30.5
24.5 –
27.5
21.5 –
24.5
18.5 –
21.5
15.5 –
18.5
12.5 –
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
I
I
II
III
III
IIII
IIII – II
IIII
III
II
II
I
I
1
1
2
3
3
4
7
5
3
2
2
1
1
35 (N or ∑f)

CUMULATIVE FREQUENCY DISTRIBUTION
1 2 3 4
Integral Limits f Cf CPf
< > < >
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
1
1
2
3
3
4
7
5
3
2
2
1
1
35
34
33
31
28
25
21
14
9
6
4
2
1
1
2
4
7
10
14
21
26
29
31
33
34
35
100.00
97.14
94.29
88.57
80.00
71.43
60.00
40.00
25.71
17.14
11.43
5.70
2.86
2.86
5.70
11.43
20.00
28.57
40.00
60.00
74.29
82.86
88.57
94.29
97.14
100
Total 35
Cumulative frequency
A frequency obtained by cumulating or
successively adding the individual frequencies
from the bottom or at the top. “Greater than”
cumulative frequency starts adding the frequency
successively from the highest class limit and “less
than” from the lowest class limit.
Cumulative Percentage frequency
is obtained by diving the cumulative frequency by
the total number of cases (N) time 100, shows the
per cent of students falling below or above (<CPf
or >CPf) certain score values.
CPf= (Cf/N)100
Legend:
f - frequency
Cf - Cumulative frequency
CPf - Cumulative Percentage frequency
< - Lesser than
> - Greater than

GRAPHICAL REPRESENTATION OF FREQUENCY
DISTRIBUTION
• Frequency Distribution are often represented
graphically to enable us to understand the essential
features of form of distributions and to compare one
frequency distribution with another with another.
• A graph is a geometrical image or a mathematical
picture of a set of data.
• For this purpose, histogram and frequency polygon
are widely used.

HISTOGRAM
• Is a graph in which the frequencies are presented by
areas in the form of vertical rectangles or bars.
• Is called a bar graph.
• Each bar is equal to the midpoint of class limit and a
height corresponding to the absolute frequency
• Midpoint is obtained by simply adding the lower limit
and upper limit and divide this by two.

HISTOGRAM
1
Integral Limits Midpoint f Cf
< >
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
47
44
41
38
35
32
29
26
23
20
17
14
11
1
1
2
3
3
4
7
5
3
2
2
1
1
35
34
33
31
28
25
21
14
9
6
4
2
1
1
2
4
7
10
14
21
26
29
31
33
34
35
Total 35

FREQUENCY POLYGON
• Is also called line graph
• Is done by plotting the frequencies with a dot at their
midpoint and connecting the plotted points by the
straight lines.
• Each frequency is plotted as a point directly above the
midpoint scores of its limit
• If there are frequencies of zero, these are plotted on
the base line.
• Then straight lines are drawn to connect the
neighboring lines.

FREQUENCY POLYGON
1
< >
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
47
44
41
38
35
32
29
26
23
20
17
14
11
1
1
2
3
3
4
7
5
3
2
2
1
1
35
34
33
31
28
25
21
14
9
6
4
2
1
1
2
4
7
10
14
21
26
29
31
33
34
35
Total 35

CUMULATIVE FREQUENCY POLYGON
• Lesser than cumulative frequency
In plotting the “lesser than” cumulative
frequency (<Cf), 35 cumulative frequency be
plotted against the top of the upper class limit
of the interval, that is 48, the frequency of 28
against 36, 25 cumulative frequency against
33, and so on.
• Greater than cumulative frequency
In plotting the “greater than” cumulative
frequency (>Cf), 1 cumulative frequency be
plotted against 4, 2 greater cumulative
frequency against 45, 4 against 42, 7 against
39 and so on.
1
< >
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
47
44
41
38
35
32
29
26
23
20
17
14
11
1
1
2
3
3
4
7
5
3
2
2
1
1
35
34
33
31
28
25
21
14
9
6
4
2
1
1
2
4
7
10
14
21
26
29
31
33
34
35
Total 35

CUMULATIVE FREQUENCY POLYGON
1
< >
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
47
44
41
38
35
32
29
26
23
20
17
14
11
1
1
2
3
3
4
7
5
3
2
2
1
1
35
34
33
31
28
25
21
14
9
6
4
2
1
1
2
4
7
10
14
21
26
29
31
33
34
35
Total 35

CUMULATIVE PERCENTAGE FREQUENCY POLYGON or
OGIVE
• Is plotted as point against the
corresponding score points at the top
of the upper class limits of the
interval.
• The lesser than cumulative frequency
(<CPf) of 100 is plotted against 48,
97.14 is plotted against 45 and so on.
On the other hand, the greater
cumulative than frequency (>CPf) of
2.86 is plotted against 48, 5.57
against 45 and so on.
1 2 3
Integral
Limits
Midpoint f CPf
< >
46 – 48
43 – 45
40 – 42
37 – 39
34 – 36
31 – 33
28 – 30
25 – 27
22 – 24
19 – 21
16 – 18
13 – 15
10 - 12
47
44
41
38
35
32
29
26
23
20
17
14
11
1
1
2
3
3
4
7
5
3
2
2
1
1
100.00
97.14
94.29
88.57
80.00
71.43
60.00
40.00
25.71
17.14
11.43
5.70
2.86
2.86
5.70
11.43
20.00
28.57
40.00
60.00
74.29
82.86
88.57
94.29
97.14
100
Total 35

Advantages and Limitations of Histogram and Polygon
Frequency polygon
• Frequency Polygon seems preferable to histogram.
• It gives a better picture of the distribution.
• The change from one point to another is direct and gives
more correct impressions
• It is advantageous also in plotting two distributions
overlapping on the same base.
• Gives a clear picture of the comparison.

Histogram
• Gives a stepwise change from one interval to another
• It gives a more readily understandable presentation of
the number of cases within each class limit; and each
measurement occupies exactly a uniform amount of
area.
• It gives a confusing picture when plotting two
distribution overlapping on the baseline.

Histogram
• It gives a confusing picture when
plotting two distribution overlapping
on the baseline.
Class Limit Midpoints
Frequency
Urban Rural
47-49
44-46
41-43
38-40
35-37
32-34
29-31
26-28
23-25
20-22
17-19
14-16
48
45
42
39
36
33
30
27
24
21
18
15
3
9
14
18
10
9
7
5
4
3
2
1
1
5
10
12
13
18
8
6
5
4
2
1

THANK YOU
FOR YOUR ATTENTION!


GROUP-10-Frequency-Distribution-and-Graphical-Representation.pptx

More Related Content

Similar to GROUP-10-Frequency-Distribution-and-Graphical-Representation.pptx

Recently uploaded

GROUP-10-Frequency-Distribution-and-Graphical-Representation.pptx