Breath Math

1. Construct histogram of variable width for the following data:

a)

CI	25-29	30-35	36-40	41-50	51-56	57-60
f	10	24	15	20	12	16

Solution:

CI	24.5-29	29.5-35.5	35.5 – 40.5	40.5-50.5	50.5-56.5	56.5-60.5
f	10	24	15	20	12	16
class width	5	6	5	10	6	4
length of  the rectangles	10	20	15	10	10	20

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(b)

CI	0 – 10	10- 15	15 – 20	20 – 30	30 – 40	40 – 60	60-70
f	20	15	10	25	5	30	50

Solution:

CI	0 – 10	10- 15	15 – 20	20 – 30	30 – 40	40 – 60	60-70
f	20	15	10	25	5	30	50
class width	10	5	5	10	10	20	10
Length of the rectangles	10	15	10	12.5	2.5	7.5	25

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2. Draw given (cumulative frequency curve) for the data given below:

Class interval	frequency
1000 – 1100	52
1100 – 1200	35
1200 – 1300	25
1300 – 1400	14
1400 – 1500	41
1500 – 1600	33

Solution:

Class interval	frequency	Cumulative frequency
1000 – 1100	52	52
1100 – 1200	35	87
1200 – 1300	25	112
1300 – 1400	14	126
1400 – 1500	41	167
1500 – 1600	33	200

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(b)

Class interval	Frequency
5 – 14	4
15 – 24	8
25 – 34	12
35 – 44	14
45 – 54	6
55 – 64	4
65 – 74	18
75 – 84	24

Solution:

Class interval	corrective factor	Frequency	cumulative frequency
5 – 14	4.5 – 14.5	4	4
15 – 24	14.5 – 24.5	8	12
25 – 34	24.5 – 34.5	12	24
35 – 44	34.5 – 44.5	14	38
45 – 54	44.5 – 54.5	6	44
55 – 64	54.5 – 64.5	4	48
65 – 74	64.5 – 74.5	18	66
75 – 84	74.5 – 84.5	24	90

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3. Construct frequency polygon for the following data :

a)

CI	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40	40 – 45
f	2	5	7	6	1	9	14	8

Solution:

(b)

CI	30-35	35-40	40-45	45-50	50-55
f	12	20	16	8	14

Solution: