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