1. Draw histogram for the distributions: (3)
Class Marks | 16 | 24 | 32 | 40 | 48 | 56 | 64 |
Frequency | 8 | 12 | 15 | 18 | 25 | 19 | 10 |
Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
Frequency | 23 | 16 | 15 | 20 | 12 |
Class Mark | 12·5 | 17·5 | 22·5 | 27·5 | 32·5 | 37·5 | 42·5 |
Frequency | 12 | 17 | 22 | 27 | 30 | 21 | 16 |
(a) From the distribution, given above, construct a frequency table.
(b) Use the table obtained in part (a) to draw: (i) a histogram, (ii) an ogive.
3. The following table shows the distribution of the heights of a
group of factory workers :
Ht.(cm): | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 | 170 - 175 | 175 - 180 | 180 - 185 |
No. of | |||||||
workers: | 6 | 12 | 18 | 20 | 13 | 8 | 6 |
(i) Determine the cumulative frequencies.
(ii) Draw the 'less than' cumulative frequency curve on graph
paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10
workers on the other. (4)
4. The following table gives the heights of plants in centimeter. If the mean height of plants is 60.95 cm; find the value of 'f'. (3)
Height (cm) | 50 | 55 | 58 | 60 | 65 | 70 | 71 |
No. of plants | 2 | 4 | 10 | f | 5 | 4 | 3 |
x | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
f | 20 | 43 | 75 | 67 | 72 | 45 | 39 | 9 | 8 | 6 |
Weekly Wages (Rs) | No. of Workers |
50-55 | 5 |
55-60 | 20 |
60-65 | 10 |
65-70 | 10 |
70-75 | 9 |
75-80 | 6 |
80-85 | 12 |
85-90 | 8 |
Calculate the mean by using:
(i) Direct Method
(ii) Short - Cut Method
or
The mean of the following distribution is 62.8 and the sum of all the frequencies is 50. Find the missing frequencies f1 and f2.
Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
Freq | 5 | f1 | 10 | f2 | 7 | 8 |
(i) Median
(ii) Upper quartile
(iii) Inter-quartile range
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83
8. The following table shows the expenditure of 60 boys on books. Find the mode of their expenditure: (3)
Expenditure (Rs) | No. of students |
20-25 | 4 |
25-30 | 7 |
30-35 | 23 |
35-40 | 18 |
40-45 | 6 |
45-50 | 2 |
Income (in thousand Rs) | 0-8 | 8-16 | 16-24 | 24-32 | 32-40 |
No. of students | 8 | 35 | 35 | 14 | 8 |
(i) Draw a cumulative frequency curve to estimate the median income.
(ii) If 15% of the students are given freeships on the basis of the basis of the income of their parents, find the annual income of parents, below which the freeships will be awarded.
(iii) Calculate the Arithmetic mean. (4)
or
he daily wages of 80 workers in a project are given below.
Wages | 400- 450 | 450- 500 | 500- 550 | 550-600 | 600-650 | 650-700 | 700- 750 |
No.of workers | 2 | 6 | 12 | 18 | 24 | 13 | 5 |
Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x - axis and 2 cm = 10 workers on y - axis). Use your ogive to estimate.
i. the median wages of the workers.
ii. the lower quartile wage of workers.
iii. the number of workers who earn more than Rs. 625 daily
10. Ramesh chooses a date at random in January for a party. (2)
January | |||||
Mon | 6 | 13 | 20 | 27 | |
Tue | 7 | 14 | 21 | 28 | |
Wed | 1 | 8 | 15 | 22 | 29 |
Thurs | 2 | 9 | 16 | 23 | 30 |
Fri | 3 | 10 | 17 | 24 | 31 |
Sat | 4 | 11 | 18 | 25 | |
Sun | 5 | 12 | 19 | 26 |
Find the probability that he chooses:
(i) a Wednesday.
(ii) a Friday.
(iii) a Tuesday or a Saturday.
11. A card is drawn from a pack of 52 cards. Find the probability that the card drawn is: (2)
(i) a red card(v) a black ace
(ii) a black card(vi) ace of diamonds
(iii) a spade(vii) not a club
(iv) an ace(viii) a queen or a jack
12. In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that: (2)
(i) it is acceptable to a trader who accepts only a good shirt?
(ii) it is acceptable to a trader who rejects only a shirt with major defects
13. Which of the following cannot be the probability of an event? (1)
(i) 3/7
(ii) 0.82
(iii) 37%
(iv) -2.4
14. A box contains a certain number of balls. Some of these balls are marked A, some are marked B and the remaining are marked C. When a ball is drawn at random from the box P(A) = 1/3 and P(B) =1/4. If there are 40 balls in the box which are marked C, find the number of balls in the box. (1)
15. A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball; find the number of black balls in the box. (2)
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