ICSE Class 10 Statistic Question set 1 FM 40

1. Draw histogram for the distributions:    (3)

Class Marks	16	24	32	40	48	56	64
Frequency	8	12	15	18	25	19	10

2. Draw frequency graph (polygon)  for each of the following distributions:  (3)

Class Interval	10-19	20-29	30-39	40-49	50-59
Frequency	23	16	15	20	12

                                                            or

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

5. Find the arithmetic mean (correct to the nearest whole-number) by using step-deviation method. (3)

x	5	10	15	20	25	30	35	40	45	50
f	20	43	75	67	72	45	39	9	8	6

6. The following table gives the weekly wages of workers in a factory. (4)

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

7.  From the following data, find:        (3)

(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

9. The income of the parents of 100 students in a class in a certain university are tabulated below.

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)