Heights in cm. | 120−124 | 125−129 | 130−134 | 135−139 | 140−144 |
No. of students | 6 | 9 | 10 | 12 | 8 |
No. of wards | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
No. of houses | 32 | 57 | 28 | 96 | 138 | 90 | 66 | 58 |
Days | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
Rainfall ( in mm) | 0.0 | 12.2 | 2.1 | 0.0 | 20.5 | 5.5 | 1.0 |
i) Find the range of the rainfall in the above data.
Class interval | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
Frequency | 3 | 7 | 12 | 15 | 8 | 3 | 2 |
Size | 10-15 | 15-20 | 20-25 | 25-30 |
Frequency | 2 | 4 | 6 | 8 |
Marks | No. of students |
0-10 | 6 |
10-20 | 5 |
20-30 | 8 |
30-40 | 15 |
40-50 | 7 |
50-60 | 6 |
60-70 | 3 |
Variate | 15 | 18 | 20 | 22 | 25 | 27 | 30 |
Frequency | 4 | 6 | 8 | 9 | 7 | 8 | 6 |
Income (in rupees) | 500-600 | 400-500 | 300-400 | 200-300 | 100-200 |
Number of persons | 17 | 20 | 30 | 18 | 15 |
Marks below | 10 | 20 | 30 | 40 | 50 |
Number of students | 3 | 8 | 17 | 20 | 22 |
Marks more than | 0 | 10 | 20 | 30 | 40 | 50 |
Number of students | 50 | 46 | 40 | 20 | 10 | 3 |
Marks | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Frequency | 3 | 8 | 10 | 12 | 16 | 12 | 10 |
Age in (years) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
Frequency | 8 | 14 | 25 | 28 | 25 | 10 | 5 |
Class interval | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
Frequency | 2 | 9 | 3 | 4 | 8 | 7 | 8 | 3 |
Find the mode of the following data.
Marks | 35 | 36 | 37 | 38 | 39 | 40 |
No of Student | 09 | 07 | 09 | 04 | 04 | 02 |
x | 3 | 4 | 5 | 6 | 7 | 8 |
f | 2 | 4 | 6 | 3 | 2 | 1 |
x | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 |
f | 20 | 50 | 80 | 60 | 15 | 8 |
No. of members | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
No. of families | 1 | 2 | 4 | 6 | 10 | 3 | 5 |
Marks | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
No. of Students | 2 | 8 | 16 | 26 | 20 | 16 | 7 | 4 |
Marks | No. of Students |
0 - 10 | 5 |
10 - 20 | 12 |
20 - 30 | 14 |
30 - 40 | 10 |
40 - 50 | 8 |
50 - 60 | 6 |
\displaystyle X_{i} | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
\displaystyle f_{i} | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
\displaystyle X_{i} | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 |
\displaystyle f_{i} | 2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |
Classes | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 |
Frequencies | 2 | 3 | 5 | 10 | 3 | 5 | 2 |
\displaystyle X_{i} | 92 | 93 | 97 | 98 | 102 | 104 | 109 |
\displaystyle f_{i} | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
Height in cms | No. of children |
70-75 | 3 |
75-80 | 4 |
80-85 | 7 |
85-90 | 7 |
90-95 | 15 |
95-100 | 9 |
100-105 | 6 |
105-110 | 6 |
110-115 | 3 |
Subject | Mathematics | Physics | Chemistry |
Mean | 42 | 32 | 40.9 |
Standard deviation | 12 | 15 | 20 |
Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Group A | 9 | 17 | 32 | 33 | 40 | 10 | 9 |
Group B | 10 | 20 | 30 | 25 | 43 | 15 | 7 |
Diameters | No. of circles |
33-36 | 15 |
37-40 | 17 |
41-44 | 21 |
45-48 | 22 |
49-52 | 25 |
X | 35 | 54 | 52 | 53 | 56 | 58 | 52 | 50 | 51 | 49 |
Y | 108 | 107 | 105 | 105 | 106 | 107 | 104 | 103 | 104 | 101 |
Marks | Up to 5 | Up to 6 | Up to 7$ | Up to 8 | Up to 9 | Up to 10 |
No of students | 5 | 11 | 19 | 31 | 40 | 45 |
98.1 | 98.6 | 99.2 | 90.3 | 86.5 | 95.3 | 92.9 | 96.3 | 94.2 | 95.1 |
89.2 | 92.3 | 97.1 | 93.5 | 92.7 | 95.1 | 97.2 | 93.3 | 95.2 | 97.3 |
96.0 | 92.1 | 84.9 | 90.0 | 95.7 | 98.3 | 97.3 | 96.1 | 92.1 | 89 |
Marks (x) | 10 | 20 | 30 | 40 | 50 | 60 |
No. of students (f) | 8 | 12 | 20 | 10 | 7 | 3 |
No. of books | 0 | 1 | 2 | 3 | 4 |
No. of students | 35 | 64 | 68 | 18 | 15 |
Wages in Rs | 30-34 | 34-38 | 38-42 | 42-46 | 46-50 | 50-54 |
No. of workers | 4 | 7 | 9 | 11 | 6 | 3 |
Class-interval | Frequency |
1-5 | 1 |
6-10 | 2 |
11-15 | 3 |
16-20 | 4 |
Class: | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 |
Frequency: | 6 | 10 | 12 | 10 | 8 |
X | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
Y | 05 | 15 | 30 | 35 | 25 | 27 | 08 |
Wages (Rs) | 125-175 | 175-225 | 225-275 | 275-325 | 325-375 | 375-425 | 425-475 | 475-525 |
Number of workers | 2 | 22 | 19 | 14 | 3 | 4 | 6 | 1 |
X=x | 1 | 2 | 3 |
p(X=x) | \frac{1}{5} | \frac{2}{5} | \frac{2}{5} |
Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
No. of student | 02 | 05 | 07 | 08 | 03 |
x_1^{} | 6 | 9 | 3 | 12 | 15 | 13 | 21 | 22 |
f_1^{} | 4 | 5 | 3 | 2 | 5 | 4 | 4 | 3 |
X=x | -2 | -1 | 0 | 1 | 2 | 3 |
P(X=x) | 0.1 | k | 0.2 | 2k | 0.3 | k |
Number of people in each car | 1 | 2 | 3 | 4 | 5 |
Frequency | 50 | 40 | 10 | 20 | 5 |
61-70 | 5 |
81-80 | 15 |
81-90 | 20 |
91-100 | 30 |
101-110 | 10 |
111-120 | 8 |
Class | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
Frequency | 3 | 7 | 12 | 15 | 8 | 3 | 2 |
x_i | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
f_i | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
x_i | 4 | 8 | 11 | 17 | 20 | 24 | 32 |
f_i | 3 | 5 | 9 | 5 | 4 | 3 | 1 |
Wages per day in Rs. | 38 | 45 | 48 | 55 | 62 | 65 |
No. of workers | 14 | 8 | 7 | 10 | 6 | 2 |
Score | 0 | 1 | 2 | 3 | 4 | 5 |
No. of shots | 0 | 3 | 6 | 4 | 7 | 5 |
Marks | 20 | 70 | 50 | 60 | 75 | 90 | 40 |
No. of students | 8 | 12 | 18 | 6 | 9 | 5 | 12 |
Marks | 35 | 45 | 50 | 64 | 70 | 72 |
No. of students | 3 | 5 | 8 | 10 | 5 | 5 |
The daily wages in (rupees of) 19 workers are
41, 21, 38, 27, 31, 45, 23, 26, 29, 30, 28, 25, 35, 42, 47, 53, 29, 31, 35.
Find the median?
Find the
mean deviation about the median for the data
x_i | 5 | 7 | 9 | 10 | 12 | 15 |
f_i | 8 | 6 | 2 | 2 | 2 | 6 |
Find the mean deviation about the mean for the data.
x | 5 | 10 | 15 | 20 | 25 |
f_{i} | 7 | 4 | 6 | 3 | 5 |
Group A | Group B |
7 | 7 |
7 | 9 |
9 | 11 |
8 | 12 |
10 | 12 |
10 | 12 |
Find the mean deviation about the median for the data
\mathrm{x_i} | 15 | 21 | 27 | 30 | 35 |
\mathrm{f}_{\mathrm{i}} | 3 | 5 | 6 | 7 | 8 |
x_i | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
f_i | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
x_i | 92 | 93 | 97 | 98 | 102 | 104 | 109 |
f_i | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Number of students | 15 | 20 | 24 | 24 | 12 | 31 | 71 | 52 |
Milk (litre) | 1 - 3 | 3 - 5 | 5 - 7 | 7 - 9 | 9 - 11 | 11 - 13 |
No. of hotels | 7 | 5 | 15 | 20 | 35 | 18 |
Average Speed of vehicles (km/hr) | 60 - 64 | 64 - 69 | 70 - 74 | 75 - 79 | 79 - 84 | 84 - 89 |
No. of vehicles | 10 | 34 | 55 | 85 | 10 | 6 |
Age (years) | :ess than 5 | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 | 25 - 29 |
No. of patients | 38 | 32 | 50 | 36 | 24 | 20 |
Use of electricity (Unit) | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 |
No of families | 13 | 50 | 70 | 100 | 80 | 17 |
Content of Fat (%) | 2 - 3 | 3 - 4 | 4 - 5 | 5 - 6 | 6 - 7 |
Milk collected (liter) | 30 | 70 | 80 | 60 | 20 |
Distance (km) | 200-210 | 210-220 | 220-230 | 230-240 | 240-250 |
No. of buses | 40 | 60 | 80 | 50 | 20 |
No. of bulbs produced (Thousands) | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
No. of factories | 12 | 35 | 20 | 15 | 8 | 7 | 8 |
No. of Cars | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
Runs scored | Number of batsmen |
3000 - 4000 | 4 |
4000 - 5000 | 18 |
5000 - 6000 | 9 |
6000 - 7000 | 7 |
7000 - 8000 | 6 |
8000 - 9000 | 3 |
9000 - 10000 | 1 |
10000 - 11,000 | 1 |
Age (in years) | No. of policy holders |
Below 20 | 2 |
Below 25 | 6 |
Below 30 | 24 |
Below 35 | 45 |
Below 40 | 78 |
Below 45 | 89 |
Below 50 | 92 |
Below 55 | 98 |
Below 60 | 100 |
Class interval | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 |
Frequency | 5 | 3 | 9 | 10 | 8 | 5 |
Age (in years) | No. of policyholders (cf) |
Below 20 | 2 |
Below 25 | 6 |
Below 30 | 24 |
Below 35 | 45 |
Below 40 | 78 |
Below 45 | 89 |
Below 50 | 92 |
Below 55 | 98 |
Below 60 | 100 |
Size | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 |
Frequency | 2 | 4 | 6 | 8 |
Diameter (mm) | 43-46 | 47-50 | 51-54 | 55-58 | 59-62 |
Number of circles | 15 | 17 | 21 | 22 | 25 |
x_{i} | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
f_{i} | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
Class | 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 |
Frequency | 5 | 7 | 18 | 25 | 20 | 4 | 1 |
Central size | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Frequency | 3 | 6 | 9 | 13 | 8 | 5 | 4 |
Central size | 32--38 | 38-44 | 44-50 | 50-56 | 56-62 | 62-68 |
No. of student | 3 | 6 | 9 | 13 | 8 | 5 |
Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
Frequency | 4 | 7 | 13 | 9 | 3 |
Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |
Frequency | 3 | 15 | 24 | 8 | 5 |
x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
f | 30 | 60 | 20 | 40 | 10 | 50 | 35 |
Class | Frequency |
10 - 15 | 3 |
15 - 20 | 7 |
20 - 25 | 16 |
25 - 30 | 12 |
30 - 35 | 9 |
35 - 40 | 5 |
40 - 45 | 3 |
Class-interval | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | 120-140 |
Frequency | 6 | 8 | 10 | 12 | 6 | 5 | 3 |
Life period (in hrs) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
Frequency | 100 | 35 | 52 | 61 | 38 | 29 |
Weight (in kg) | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 |
No. of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
Height (in cm) | 52 - 55 | 55 - 58 | 58 - 61 | 61 - 64 |
No. of students | 10 | 20 | 25 | 10 |
Marks | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
No. of students | 4 | 28 | 42 | 20 | 6 |
Class-interval | Frequency |
80-85 | 33 |
85-90 | 27 |
90-95 | 85 |
95-100 | 155 |
100-105 | 110 |
105-110 | 45 |
110-115 | 15 |
Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
Students | 19 | 3 | 2 | 49 | 24 | 5 | 2 | 1 |
X | 10 | 20 | 30 | 40 | 50 | 60 |
Class |
Frequency (f) |
0-10 |
5 |
10-20 |
8 |
20-30 |
15 |
30-40 |
16 |
40-50 |
6 |
Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Number of students | 1 | 2 | 3 | 3 | 6 | 10 | 5 | 4 | 3 | 3 |
Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Number of students | 1 | 2 | 3 | 3 | 6 | 10 | 5 | 4 | 3 | 3 |
Roll No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Marks | 50 | 45 | 60 | 40 | 40 | 60 | 65 | 50 | 56 | 70 |
Class | Frequency |
0-10 | 5 |
10-20 | 8 |
20-30 | 10 |
30-40 | 15 |
40-50 | 12 |
Class |
Frequency |
10-20 |
4 |
20-30 |
5 |
30-40 |
6 |
40-50 |
2 |
50-60 |
3 |
Class | Frequency (f) |
10-20 | 4 |
20-30 | 5 |
30-40 | 6 |
40-50 | 2 |
50-60 | 3 |
Class | Frequency |
0-10 | 5 |
10-20 | 8 |
20-30 | 10 |
30-40 | 15 |
40-50 | 12 |
Weeks | COVID Patients (‘000) |
0-4 | 600 |
4-8 | 400 |
8-12 | 250 |
12-16 | 200 |
16-20 | 300 |
20-24 | 350 |
24-28 | 450 |
28-32 | 500 |
32-36 | 750 |
36-40 | 900 |
Marks | No. Of students |
0-20 | 8 |
20-40 | 12 |
40-60 | 30 |
60-80 | 20 |
80-100 | 10 |
No. of Books | 0 | 1 | 2 | 3 | 4 |
No. of Students | 35 | 64 | 68 | 18 | 15 |
x | 3 | 8 | 13 | 18 | 23 |
f | 7 | 10 | 15 | 10 | 8 |
x | 3 | 8 | 13 | 17 | 23 |
f | 7 | 10 | 15 | 10 | 8 |
Wages (Rs) | 125-175 | 175-225 | 225-275 | 275-325 | 325-375 | 375-425 | 425-475 | 475-525 | 525-575 |
Number of workers | 2 | 22 | 19 | 14 | 3 | 4 | 6 | 1 | 1 |
{ x }_{ i } | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
{ f }_{ i } | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
x=x | -2 | -1 | 0 | 1 | 2 | 3 |
P(x) | 0.1 | k | 0.2 | 2k | 0.3 | k |
Class | 0-10 | 10-20 | 20-20 | 30-40 | 40-50 |
Frequency | 5 | 8 | 15 | 16 | 6 |
Marks (Less than) |
Number of students (f) |
20 |
8 |
40 |
20 |
60 |
50 |
80 |
70 |
100 |
80 |
Class Interval | Frequency |
0-5 | 15 |
5-10 | 10 |
10-15 | 11 |
15-20 | 12 |
20-25 | 6 |
25-30 | 6 |
30-35 | 10 |
35-40 | 15 |
40-45 | 10 |
45-50 | 5 |
Class | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |
Frequency | 64 | 132 | 153 | 140 | 51 |
No. of Mangoes | 50 - 100 | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 |
No. of trees | 33 | 30 | 90 | 80 | 17 |
Size | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Frequency | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
Size | 4 | 6 | 8 | 10 | 12 | 14 | 16 |
Frequency | 1 | 2 | 3 | 5 | 3 | 2 | 1 |