Question

Marks scored by 50 students are given below:

40	45	38	24	46	42	45	18	53	64
45	32	52	54	78	65	52	64	66	43
48	55	50	43	48	20	27	65	37	55
51	55	62	66	38	16	60	58	46	35
72	62	54	58	30	36	43	82	46	53

(a) Arrange the marks in ascending order.
(b) Represent the marks in the form of discrete frequency distribution.
(c) Construct an inclusive frequency distribution with first class as 10−19. Also construct class boundaries.
(d) Construct a frequency distribution with exclusive class-intervals, taking the lowest class as 10−20.
(e) Convert the exclusive series constructed in (d) into 'less than' and 'more than' cumulative frequency distribution.

Answer 1

(a)

Marks arranged in ascending order
16 18 20 24 27 30 32 35 36 37 38 38 40 42 43 43 43 45 45 45 46 46 46 48 48	50 51 52 52 53 53 54 54 55 55 55 58 58 60 62 62 64 64 65 65 66 66 72 78 82

(b)

Discrete Frequency Distribution

Marks	Frequency (f)
16 18 20 24 27 30 32 35 36 37 38 40 42 43 45 46 48 50 51 52 53 54 55 58 60 62 64 65 66 72 78 82	1 1 1 1 1 1 1 1 1 1 2 1 1 3 3 3 2 1 1 2 2 2 3 2 1 2 2 2 2 1 1 1
	$\sum _{}^{}f=50$

(c)
Inclusive Frequency Distribution

Class Interval (Marks)	No. of Students
10 − 19 20 − 29 30 − 39 40 − 49 50 − 59 60 − 69 70 − 79 80 − 89	2 3 7 13 13 9 2 1
	$\sum _{}^{}f=50$

(d)
Exclusive Frequency Distribution

Class Interval	No. of Students
10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 80 −90	2 3 7 13 13 9 2 1
	$\sum _{}^{}f=50$

(e)
Less than frequency distribution

Marks	Cumulative Frequency
Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 Less than 90	2 2 + 3 = 5 5 + 7 = 12 12 + 13 = 25 25 + 13 = 38 38 + 9 = 47 47 + 2 = 49 49 + 1 = 50

More than frequency distribution

Marks	Cumulative Frequency
More than 10 More than 20 More than 30 More than 40 More than 50 More than 60 More than 70 More than 80	50 50 − 2 = 48 48 − 3 = 45 45 − 7 = 38 38 − 13 = 25 25 − 13 = 12 12 − 9 = 3 3 − 2 =1