Question 1

Q1: A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding...

Accepted Answer

Given: The data regarding the number of plants in 20 houses. To Find: The mean number of plants per house. Solution: We will use the direct method to find the mean as the numerical values of the frequency ($f_i$) and the class mark ($x_i$) are small. First, we find the class mark ($x_i$) for each cl...

Question 2

Q2: Consider the following distribution of daily wages of 50 workers of a factory. | Daily wages (in ₹) | 500-520 | 520-540 | 540-560 | 560-580 | 580-600...

Accepted Answer

Given: The distribution of daily wages of 50 workers. To Find: The mean daily wages of the workers. Solution: Since the values of the class marks ($x_i$) will be large, we will use the Step-Deviation Method to simplify the calculations. The class size is uniform, $h = 20$. Let's choose an assumed me...

Question 3

Q3: The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency...

Accepted Answer

Given: The distribution of daily pocket allowance of children, with a missing frequency $f$. The mean pocket allowance is ₹ 18. To Find: The value of the missing frequency $f$. Solution: We will use the direct method. First, let's create a table to organize the calculations. | Daily pocket allowance...

Question 4

Q4: Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean he...

Accepted Answer

Given: The distribution of heartbeats per minute for 30 women. To Find: The mean heartbeats per minute. Solution: The class marks ($x_i$) are not very large, but to simplify calculations, we can use the Assumed Mean Method. The class size is uniform, $h = 3$. Let's choose an assumed mean, $a$. The c...

Question 5

Q5: In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the d...

Accepted Answer

Given: The distribution of mangoes in packing boxes. To Find: The mean number of mangoes per box. Solution: The given class intervals are not continuous. We need to make them continuous by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class. | Number of mangoes | Con...

Question 6

Q6: The table below shows the daily expenditure on food of 25 households in a locality. | Daily expenditure (in ₹) | 100-150 | 150-200 | 200-250 | 250-300...

Accepted Answer

Given: The daily expenditure on food of 25 households. To Find: The mean daily expenditure on food. Solution: We will use the Step-Deviation Method because the class marks are large numbers. The class size is uniform, $h = 50$. Let's choose an assumed mean, $a$. The class marks are 125, 175, 225, 27...

Question 7

Q7: To find out the concentration of SO$_2$ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and i...

Accepted Answer

Given: The data for the concentration of SO$_2$ in the air for 30 localities. To Find: The mean concentration of SO$_2$ in the air. Solution: The class marks are small decimal numbers, so the direct method is suitable for this calculation. Let's create a table to calculate the mean: | Concentration...

Question 8

Q8: 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. | N...

Accepted Answer

Given: The absentee record of 40 students. To Find: The mean number of days a student was absent. Solution: The class sizes are not uniform (6, 4, 4, 6, 8, 10, 2). Therefore, the step-deviation method is not directly applicable in its usual form. The direct method is the most reliable method here. L...

Question 9

Q9: 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...

Accepted Answer

Given: The literacy rate of 35 cities. To Find: The mean literacy rate. Solution: We will use the Step-Deviation Method to find the mean. The class size is uniform, $h = 10$. Let's choose an assumed mean, $a$. The class marks are 50, 60, 70, 80, 90. Let's take $a = 70$. Let's create the table for ca...

Question 10

Q1: The following table shows the ages of the patients admitted in a hospital during a year: | Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-...

Accepted Answer

Given: The ages of patients admitted to a hospital. To Find: The mode and the mean of the data, and to compare and interpret them. Part 1: Finding the Mode The class with the maximum frequency is the modal class. From the table, the maximum frequency is 23, which corresponds to the class interval 35...

Question 11

Q2: The following data gives the information on the observed lifetimes (in hours) of 225 electrical components : | Lifetimes (in hours) | 0-20 | 20-40 | 4...

Accepted Answer

Given: The observed lifetimes of 225 electrical components. To Find: The modal lifetimes of the components. Solution: To find the mode, we first identify the modal class, which is the class with the highest frequency. From the table, the maximum frequency is 61. The corresponding class interval is 6...

Question 12

Q3: The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of t...

Accepted Answer

Given: The distribution of total monthly household expenditure of 200 families. To Find: The modal and mean monthly expenditure. Part 1: Finding the Mode The maximum frequency is 40, which corresponds to the class interval 1500-2000. So, the modal class is 1500-2000. We have: $l = 1500$ $f_1 = 40$ $...

Question 13

Q4: The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Inter...

Accepted Answer

Given: State-wise teacher-student ratio. To Find: The mode and mean of the data and interpret them. Part 1: Finding the Mode The maximum frequency is 10, corresponding to the class interval 30-35. So, the modal class is 30-35. We have: $l = 30$ $f_1 = 10$ $f_0 = 9$ $f_2 = 3$ $h = 5$ Formula for Mode...

Question 14

Q5: The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. | Runs scored | Numb...

Accepted Answer

Given: The distribution of runs scored by top batsmen. To Find: The mode of the data. Solution: The maximum frequency is 18, which corresponds to the class interval 4000-5000. So, the modal class is 4000-5000. We have: Lower limit of the modal class, $l = 4000$ Frequency of the modal class, $f_1 = 1...

Question 15

Q6: A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find...

Accepted Answer

Given: The number of cars passing through a spot for 100 periods. To Find: The mode of the data. Solution: The maximum frequency is 20, which corresponds to the class interval 40-50. So, the modal class is 40-50. We have: Lower limit of the modal class, $l = 40$ Frequency of the modal class, $f_1 =...

Question 16

Q1: The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the...

Accepted Answer

Given: The monthly electricity consumption of 68 consumers. To Find: The median, mean, and mode of the data and compare them. First, let's create a comprehensive table for all calculations. Total number of consumers, $n = \Sigma f_i = 68$. Class size, $h = 20$. Let's choose assumed mean $a = 135$. |...

Question 17

Q2: If the median of the distribution given below is 28.5, find the values of $x$ and $y$. | Class interval | Frequency | |---|---| | 0-10 | 5 | | 10-20 |...

Accepted Answer

Given: A frequency distribution with median = 28.5 and total frequency = 60. To Find: The values of the missing frequencies $x$ and $y$. Solution: First, we create the cumulative frequency table. | Class interval | Frequency ($f_i$) | Cumulative Frequency (cf) | |---|---|---| | 0-10 | 5 | 5 | | 10-2...

Question 18

Q3: A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only t...

Accepted Answer

Given: A cumulative frequency distribution of the 'less than' type for the ages of 100 policy holders. To Find: The median age. Solution: First, we need to convert the given cumulative frequency data into a frequency distribution table with class intervals. The policies start from age 18. So the fir...

Question 19

Q4: 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 : | Le...

Accepted Answer

Given: The lengths of 40 leaves with discontinuous class intervals. To Find: The median length of the leaves. Solution: The class intervals are not continuous. The gap between the upper limit of a class and the lower limit of the next class is 1 (e.g., 127 - 126 = 1). We make the data continuous by...

Question 20

Q5: The following table gives the distribution of the life time of 400 neon lamps : | Life time (in hours) | Number of lamps | |---|---| | 1500-2000 | 14...

Accepted Answer

Given: The distribution of the lifetime of 400 neon lamps. To Find: The median lifetime of a lamp. Solution: Let's create the cumulative frequency table. | Life time (in hours) | Number of lamps ($f_i$) | Cumulative Frequency (cf) | |---|---|---| | 1500-2000 | 14 | 14 | | 2000-2500 | 56 | $14+56=70$...

Concentration of SO $_2$ (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

Expenditure (in ₹)	Number of families
1000-1500	24
1500-2000	40
2000-2500	33
2500-3000	28
3000-3500	30
3500-4000	22
4000-4500	16
4500-5000	7

Number of students per teacher	Number of states / U.T.
15-20	3
20-25	8
25-30	9
30-35	10
35-40	3
40-45	0
45-50	0
50-55	2

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
10000-11000	1

Monthly consumption (in units)	Number of consumers
65-85	4
85-105	5
105-125	13
125-145	20
145-165	14
165-185	8
185-205	4

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	92
Below 55	98
Below 60	100

Length (in mm)	Number of leaves
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-171	4
172-180	2

NCERT Solutions