Q. A survey was conducted by a group of students as a part of their environmental awareness programme, in which they collected the following data regarding the number of plants in 20 houses of a locality. Find the mean number of plants per house.

Number of Plants Number of Houses
0 โ€“ 2 1
2 โ€“ 4 2
4 โ€“ 6 1
6 โ€“ 8 5
8 โ€“ 10 6
10 โ€“ 12 2
12 โ€“ 14 3

Ans. 8 plants.

Q. Thirty women were examined in a hospital by a doctor and the number of heart-beats per minute were recorded and summarised as follows. Find the mean heart-beats per minute.

Heart-beats per minute Number of Women
65 โ€“ 68 2
68 โ€“ 71 4
71 โ€“ 74 3
74 โ€“ 77 8
77 โ€“ 80 7
80 โ€“ 83 4
83 โ€“ 86 2

Ans. 75.9 heart-beats per minute.

Q. The following distribution shows the daily pocket allowance given to the children of a multi-storey building. The average pocket allowance is โ‚น 18. Find out the missing frequency.

Class Interval Frequency
11 โ€“ 13 7
13 โ€“ 15 6
15 โ€“ 17 9
17 โ€“ 19 13
19 โ€“21 f
21 โ€“ 23 5
23 โ€“ 25 4

Ans. 20.

Q. In the retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was their distribution according to the number of boxes.

No. of Mangoes No. of Boxes
50 โ€“ 52 15
53 โ€“ 55 110
56 โ€“ 58 135
59 โ€“ 61 115
62 โ€“ 64 25

Find the mean number of mangoes kept in a packing box.

Ans. 50.

Q. The table below shows the daily expenditure on food of 25 households in a locality. Find the mean expenditure.

Expenditure Number of Households
100 โ€“ 150 4
150 โ€“ 200 5
200 โ€“ 250 12
250 โ€“ 300 2
300 โ€“ 350 2

Ans. โ‚น 211.

ย 

Q. A class teacher has the following absentee record of 40 students for the whole term. Find the mean number of days a student remained absent.

Number of Days Number of Students
0 โ€“ 6 11
6 โ€“ 10 10
10 โ€“ 14 7
14 โ€“ 20 4
28 โ€“ 38 3
38 โ€“ 40 1
20 โ€“ 28 4

Ans. 12.475 days.

ย 

Q. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy % Cities
45 โ€“ 55 3
55 โ€“ 65 10
65 โ€“ 75 11
75 โ€“ 85 8
85 โ€“ 95 3

Ans. 69.43%.

Q. If the median of the distribution given below is 28.5 and ฮฃfi = 60, find the value of x and y.

Class Interval Frequency
0 โ€“ 10 5
10 โ€“ 20 x
20 โ€“ 30 20
30 โ€“ 40 15
40 โ€“ 50 y
50 โ€“ 60 5

Ans. x = 8, y = 7.

Q. A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons in the age group of 18 to 60 years.

Age (in years) Number of Policy-holders
Below 20 2
Below 25 6
Below 30 24
Below 35 45
Below 40 78
Below 45 89
Below 50 98
Below 60 100

Ans. 35.76 years.

Q. The lengths of 40 leaves of a plant are measured correct to the nearest millimetre and the data obtained is represented in the following table. Find the median length of the leaves.

Length (in mm) Number of Leaves
Below 20 2
118 โ€“ 126 3
127 โ€“ 135 5
136 โ€“ 144 9
145 โ€“ 153 12
154 โ€“ 162 5
163 โ€“ 171 4
172 โ€“ 180 4

Ans. 146.75 mm.

Q. The following table gives the distribution of the life time (in hours) of 400 neon lamps. Find the median life time of a lamp.

Life time (in hours) Number of Lamps
1500 โ€“ 2000 14
2000 โ€“ 2500 56
2500 โ€“ 3000 5
3000 โ€“ 3500 86
3500 โ€“ 4000 74
4000 โ€“ 4500 62
4500 โ€“ 5000 48

Ans. 3406.98 hours.

Q. The following distribution gives the weight (in kg) of 30 students in a class. Find the median weight of the students.

Weight (in kg) Number of Students
40 โ€“ 45 2
45 โ€“ 50 3
50 โ€“ 55 8
55 โ€“ 60 6
60 โ€“ 65 6
65 โ€“ 70 3
70 โ€“ 75 2

Ans. 56.67 kg.

Q. The following data gives the distribution of the total household expenditure (in rupees) of manual workers in a city:

Expenditure (in Rupees) Frequency
1000 โ€“ 1500 24
1500 โ€“ 2000 40
2000 โ€“ 2500 33
2500 โ€“ 3000 28
3000 โ€“ 3500 30
3500 โ€“ 4000 22
4000 โ€“ 4500 16
4500 โ€“ 5000 7

Find the mode of the average expenditure of the families.

Ans. โ‚น 1847.83.

Q. The following table shows the ages of the patients admitted to a hospital during a year.

Ages (in years) Number of Patients
5 โ€“ 15 6
15 โ€“ 25 11
25 โ€“ 35 21
35 โ€“ 45 23
45 โ€“ 55 14
55 โ€“ 65 5

Find the mean and mode of the data given above.

Ans. Mean = 35.375, Mode = 36.8

Q. The following distribution provides information about the observed lifetime (in hours) of 225 electrical components. Determine the modal lifetime of the components.

Lifetime (in years) Number of Components
0 โ€“ 20 10
20 โ€“ 40 35
40 โ€“ 60 52
60 โ€“ 80 61
80 โ€“ 100 38
100 โ€“ 120 29

Ans. 65.625 hours.

Q. The following distribution gives the state-wise teacher-student ratio in higher-secondary schools of India. Find the mean and mode from the data.

Number of Students/Teachers Number of States/U.T.s
15 โ€“ 20 3
20 โ€“ 25 8
25 โ€“ 30 9
30 โ€“ 35 10
35 โ€“ 40 3
40 โ€“ 45 0
45 โ€“ 50 0
50 โ€“ 55 2

Ans. Mean = 29.2, Mode = 30.6

Q. The following data shows the number of runs scored in ODI cricket by some of the top batsmen of the world:

Runs Scored Number of Batsmen
3000 โ€“ 4000 4
4000 โ€“ 5000 18
5000 โ€“ 6000 9
6000 โ€“ 7000 7
7000 โ€“ 8000 6
8000 โ€“ 9000 3
9000 โ€“ 10000 1
10000 โ€“ 11000 1

Find the mode of the data.

Ans. 4608.7 runs.

Q. A student noted the number of cars passing through a spot on a road for 100 periods, each of 3 minutes and summarized it in the table given below. Find the mode.

Number of Cars Frequency
0 โ€“ 10 7
10 โ€“ 20 14
20 โ€“ 30 13
30 โ€“ 40 12
40 โ€“ 50 20
50 โ€“ 60 11
60 โ€“ 70 15
70 โ€“ 80 8

Ans. Mode = 44.71 cars โ‰ˆ 45 cars.