STATISTICS
Q1. Calculate the mean for the following distribution:
x: |
5 |
6 |
7 |
8 |
9 |
f: |
4 |
8 |
14 |
11 |
3 |
Q2. If the mean of the following data is 20.6. Find the value of p.
x: |
10 |
15 |
p |
25 |
35 |
f: |
3 |
10 |
25 |
7 |
5 |
Q3. Find the value of p for the following distribution whose mean is 16.6
x: |
8 |
12 |
15 |
p |
20 |
25 |
30 |
f. |
12 |
16 |
20 |
24 |
16 |
8 |
4 |
Q4. Find the missing frequency
(p) for the following distribution whose mean is 7.68.
x: |
3 |
5 |
7 |
9 |
11 |
13 |
f: |
6 |
8 |
15 |
p |
8 |
4 |
Q5. Find the value of p, if the mean of the following
distribution is 20.
x: |
15 |
17 |
19 |
20 +
p |
23 |
f: |
2 |
3 |
4 |
5p |
6 |
Q6. The
following table gives the number of boys of a particular age in a class of 40 students.
Calculate the mean age of the students
Age
(in years): 15 |
16 |
17 |
18 |
19 |
20 |
No.
of students: 3 |
8 |
10 |
10 |
5 |
4 |
Q7. Find the missing frequencies in the following
frequency distribution if it is known that the mean of the distribution is 50.
X:
10 |
30 |
50 |
70 |
90 |
|
f: 17 |
f1 |
32 |
f2 |
19 |
Total
120. |
Q8. The
arithmetic mean of the following data is
14. Find the value of k
𝑥𝑖: |
5 |
10 |
15 |
20 |
25 |
𝑓𝑖: |
7 |
k |
8 |
4 |
5. |
𝑥𝑖: |
5 |
15 |
25 |
35 |
45 |
𝑓𝑖: |
3 |
k |
3 |
6 |
2 |
Q10. If the mean of the following data is 18.75. Find the value of p.
𝑥𝑖: |
10 |
15 |
p |
25 |
30 |
𝑓𝑖: |
5 |
10 |
7 |
8 |
2 |
Q11. Five coins were simultaneously
tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during
which 0,1,2,3,4 and 5 heads
were obtained are shown in
the table below. Find the mean number of heads per toss
No.
of heads per toss (x): |
0 |
1 |
2 |
3 |
4 |
5 |
No.
of tosses (f): |
38 |
144 |
342 |
287 |
164 |
25 |
Q12. The marks obtained out of 50, by 102 students in a Physics
test are given in
the frequency table below:
Marks(x): |
15 |
20 |
22 |
24 |
25 |
30 |
33 |
38 |
45 |
Frequency (f): |
5 |
8 |
11 |
20 |
23 |
18 |
13 |
3 |
1 |
Find the average
number of marks.
Q13. The number of students
absent in a class were recorded every
day for 120 days
and the information is given in the
following frequency table:
No.
of students absent
(x): |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
No.
of days(f): |
1 |
4 |
10 |
50 |
34 |
15 |
4 |
2 |
Find
the mean number
of students absent per day.
Q14. In
the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:
No.
of misprints per
page (x): 0 |
1 |
2 |
3 |
4 |
5 |
No.
of pages (f): 154 |
95 |
36 |
9 |
5 |
1 |
Find the average
number of misprints per page.
Q15. The following distribution gives the number
of accidents met by 160 workers in a factory during a month.
No.
of accidents (x): |
0 |
1 |
2 |
3 |
4 |
No.
of workers (f): |
70 |
52 |
34 |
3 |
1 |
Find the average number of accidents per worker.
Q16. Find the mean from the following frequency distribution of marks at a test in
statistics:
Marks(x): |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
No.
of students (f): |
15 |
50 |
80 |
76 |
72 |
45 |
39 |
9 |
8 |
6 |
Q17. The following table gives the distribution of total household expenditure (in rupees)
of manual workers in a city.
Expenditure (in rupees) (x) |
Frequency (fi) |
Expenditure (in rupees) (x1) |
Frequency (fi) |
100 – 150 |
24 |
300
– 350 |
30 |
150 – 200 |
40 |
350
– 400 |
22 |
200
– 250 |
33 |
400
– 450 |
16 |
250 – 300 |
28 |
450
– 500 |
7 |
Find the average expenditure (in rupees) per
household.
Q18. A survey was conducted by a
group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants
in 20 houses in a locality. Find the
mean number of plants per house.
Number of plants: |
0-2 |
2-4 |
4-6 |
6-8 |
8-10 |
10-12 12-14 |
Number of houses: |
1 |
2 |
1 |
5 |
6 |
2 3 |
Which
method did you use for finding
the mean, and why?
Q19. Consider the following distribution of daily wages of 50 workers of a factory.
Daily wages (in Rs). 100 - 120 120 - 140 140 - 160 160 - 180 180 - 200
Number of workers: 1 2 14 8 6 10
Find
the mean daily wages of the workers of the factory by using an appropriate method.
Q20. Find the mean of each of the following frequency distributions: (5 − 14)
I. |
Class interval: |
0
- 6 |
6
- 12 |
12
- 18 |
18
- 24 |
24-30 |
|
Frequency: |
6 |
8 |
10 |
9 |
7 |
II. Class interval:
50 - 70 70 - 90 90
– 110
110 - 130 130
- 150 150 – 170
Frequency: 18 12 13 27 8 22
III. |
Class interval: 0-8 |
8- 16 |
16- 24 |
24-32 |
32-40 |
|
Frequency: 6 |
7 |
10 |
8 |
9 |
IV. |
Class interval: 0-6 |
6-
12 |
12- 18 |
18-24 |
24-30 |
|
Frequency: 7 |
5 |
10 |
12 |
6 |
V. |
Class interval: |
0- 10 |
10- 20 |
20-30 |
30-40 |
40-50 |
|
Frequency: |
9 |
12 |
15 |
10 |
14 |
VI.
Class interval: 0-8 8- 16 16-24 24-32 32 -40
Frequency: 5 9 10 8 8
|
VII. |
Class interval: |
0-8 |
8- 16 |
16- 24 |
24-32 |
32-40 |
|||||
|
|
Frequency: |
5 |
6 |
4 |
3 |
2 |
|||||
VIII. Class interval: 10-30 30-50 |
50-70 |
70-90 |
90-110 |
110- 130 |
|
|||||||
Frequency: 5 8 |
12 |
20 |
3 |
2 |
|
|||||||
IX. Class interval:
25-35 35-45 45-55 55
- 65 65 – 75
Frequency:
6 10 8
12 4
X. |
Classes: |
25
-29 30-34 |
35-39 |
40-44 |
45-49 |
50-54 |
55-59 |
|
Frequency: |
14 22 |
16 |
6 |
5 |
3 |
4 |
Q21. For the following distribution, calculate mean using all suitable
methods:
Size
of item: |
1 -4 |
4-9 |
9-
16 |
16-27 |
Frequency: |
6 |
12 |
26 |
20 |
Q22. The following table shows the marks scored by 140 students
in an examination of a certain paper:
Marks: 0-
10
10-20 20-30 30-40 40-50
Number
of students: 20 24 40 36 20
Calculate the average marks by using all the three methods:
direct method, assumed mean deviation and shortcut
method.
Q23. The mean of the following frequency distribution is 62.8 and the sum of all the frequencies
is 50. Compute
the missing frequency f1 and f2.
Class: |
0 -
20 |
20 -
40 |
40 -
60 |
60 -
80 |
80 -
100 |
100 – 120 |
Frequency: |
5 |
f1 |
10 |
f2 |
7 |
8 |
Q24. The following distribution shows
the daily pocket
allowance given to the children
of a multistorey building. The average pocket allowance is
Rs 18.00. Find out the missing frequency.
Class
interval: 11-13 13-15 15-17 17-19 19-21 21-23 23-25
Frequency: 7 6 9 13 - 5 4
Q25. If the mean of the following
distribution is 27, find the value of p.
Class: 0 - 10 10 – 20 20 - 30 30
– 40 40-50
Frequency: 8 p
12 13 10
Q26. In a retail market, fruit vendors
were selling mangoes kept in packing boxes. These boxes contained varying
number of mangoes. The following was the distribution of mangoes according to
the number of boxes.
Number
of mangoes: 50
- 52 53 – 55 56 - 58 59 - 61 62 -64
Number
of boxes: 15
110 135 115
25
Find
the mean number of mangoes
kept in a packing box. Which method of finding
the mean did you choose?
Q27. The table below shows the daily expenditure on food of 25 households in a locality
Daily
expenditure (in Rs): 100
- 150 150 - 200 200 - 250 250 - 300 300 -350
Number of households: 4 5 12
2 2
Find
the mean daily expenditure on food by a suitable
method.
Q28. A
class teacher has the following absentee record of 40 students
of a class for the whole term. Find the mean number of days
a student was absent.
Number of days: |
0
- 6 |
6
- 10 |
10
- 14 |
14 - 20 |
20 -28 |
28
- 38 |
38
- 40 |
Number of students: |
11 |
10 |
7 |
4 |
4 |
3 |
1 |
Q29. Following are the lives
in hours of 15 pieces
of the components of aircraft
engine. Find the median:
715, 724, 725, 710, 729, 745, 694, 699,
696, 712, 734, 728, 716, 705, 719.
Q30. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy rate (in %): 45 - 55 55
- 65
65 -
75
75 - 85 85 -95
Number
of cities: 3 10
11 8 3
Q31. To
find out the concentration of SO2 in the air (in parts
per million, i.e.,
ppm), the data was collected for 30 localities in a
certain city and is presented below:
Concentration of SO2 (in ppm) |
Frequency |
0.00-0.04 |
4 |
0.04-0.08 |
9 |
0.08-0.12 |
9 |
0.12-0.16 |
2 |
0.16-0.20 |
4 |
0.20-0.24 |
2 |
Find the mean concentration of SO2 in the air.
Q32. Following is the distribution of I.Q. of loo students. Find the median I.Q.
I.Q.: 55-64
65-74 75-84 85-94 95-104 105-114 115-124
125-134 135-144
No of Students: 1 2
9 22
33 22 8 2 1
Q33. Calculate the median from the following data:
Rent
(in Rs.): |
15-25 |
25-35 |
35-45 |
45-55 |
55-65 |
65-75 |
75-85 |
85-95 |
No.
of Houses: |
8 |
10 |
15 |
25 |
40 |
20 |
15 |
7 |
Q34. Calculate the median from the following data:
Marks
below: |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
No.
of students: |
15 |
35 |
60 |
84 |
96 |
127 |
198 |
250 |
Q35. An
incomplete distribution is given as follows:
Variable : 0 – 10 10 - 20 20 – 30 30 - 40 40 – 50 50 - 60 60 - 70
Frequency: 10 20 ?
40 ? 25 15
You are given that the median value
is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the
missing frequencies.
Q36. Calculate the missing frequency
from the following
distribution, it being
given that the median of the distribution is 24.
Age
in years: 0 - 10 |
10 -
20 |
20 -
30 |
30 -
40 |
40-50 |
No.
of persons: 5 |
25 |
? |
18 |
7 |
Q36. Find the missing frequencies and the median
for the following distribution if the mean is
1.46.
No.
of accidents: |
0 |
1 |
2 |
3 |
4 |
5 |
Total |
Frequency (No. of days): |
46 |
? |
? |
25 |
10 |
5 |
200 |
Q38. If
the median of the following
frequency distribution is 28.5 find the missing
frequencies:
Class interval: 0-10 10-20 20-30
30-40 40-50 50-60 Total
Frequency: 5
f1 20 15 f2 5 60
Q39. The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the
data:
Class interval |
Frequency |
Class interval |
Frequency |
0-100 |
2 |
500-600 |
20 |
100-200 |
5 |
600-700 |
f2 |
200-300 |
f1 |
700-800 |
9 |
300-400 |
12 |
800-900 |
7 |
Q40. If the median of the following data
is 32.5, find the missing frequencies.
Class interval: 0- 10 10-20 20-30 30-40 40-50 50-60 60-70
Total
Total Frequency: f1 5 9 12 f2 3 2 40