15. Frequency Distribution Unit.no.1


15. Frequency Distribution:
(a)   Frequency Distribution of Discrete Data: There are no class boundaries because discrete data are not in fractions.  If class interval size is one we usually take single values. 
No. of children in a family
Number of families
0
7
1
3
2
25
3
16
4
9
5
4
6
1
Total
65
(b)   Frequency Distribution of Continuous Data: Class boundaries are formed for continuous data because the continuous data are in fractions:
Heights of students in a class (inches)
Number of students
55.5-58.0
1
58.0-60.5
6
60.5-63.0
17
63.0-65.5
18
65.5-68.0
18
68.0-70.5
4
70.5-73.0
1
Total (S f)
65
(c)    Cumulative Frequency Distribution: is the table showing cumulative frequencies:
Heights (inches)
No. of students
Less than
Cumulative
Frequency
Heights (inches)
No. of students
Greater than
Cumulative
Frequency
Less than 55.5
0
55.5 and more
65
Less than 58.0
1
58.0 and more
64
Less than 60.5
7
60.5 and more
58
Less than 63.0
24
63.0 and more
41
Less than 65.5
42
65.5 and more
23
Less than 68.0
60
68.0 and more
5
Less than 70.5
64
70.5 and more
1
Less than 73.0
65
73.0 and more
0
(d)   Relative Frequency Distribution: is expressed in percentage of frequency to total frequency:
Heights
Frequency
(No. of students)
Relative frequency
(%)
55.5-58.0 1 1 / 65 × 100 = 1.54
58.0-60.5 6 6 / 65 × 100 = 9.23
60.5-63.0 17 26.15
63.0-65.5 18 27.69
65.5-68.0 18 27.69
68.0-70.5 4 6.16
70.5-73.0 1 1.54

65 100
(e)   Relative Cumulative Frequency Distribution:
Heights
(Inches)
No. of students
Less than
Cumulative
Frequency
Relative
Frequency
Heights
(Inches)
No. of students
Greater than
Cumulative
Frequency
Relative
Frequency
Less than 55.5
0
0
55.5 and more
65
100
Less than 58.0
1
1 / 65 × 100 = 1.54
58.0 and more
64
98.46
Less than 60.5
7
7 / 65 × 100 = 10.77
60.5 and more
58
89.23
Less than 63.0
24
36.92
63.0 and more
41
63.08
Less than 65.5
42
64.61
65.5 and more
23
35.38
Less than 68.0
60
92.31
68.0 and more
5
7.69
Less than 70.5
64
98.46
70.5 and more
1
1.54
Less than 73.0
65
100
73.0 and more
0
0
(f)     Bivariate Frequency Distribution: involves constructing frequency distribution of two variables:
Weights
(pounds)
Heights (inches)
57-59
60-62
63-65
66-68
69-71
72-74
Total
100-104
3
7
-
-
-
-
10
105-109
-
5
10
2
1
-
18
110-114
1
1
4
6
4
0
14
115-119
-
-
1
1
4
2
8
Total
3
12
15
9
9
2
50

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