- 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 |
(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 |
- 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 |
(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 |
- 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:
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