# NCERT Solutions for Class 10 Maths Unit 14

## Statistics Class 10

### Exercise 14.1 : Solutions of Questions on Page Number : 270

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 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?

To find the class mark (xi) for each interval, the following relation is used.

Class mark (xi) =

xi andfixi can be calculated as follows.

 Number of plants Number of houses (fi) xi fixi 0 - 2 1 1 1 × 1 = 1 2 - 4 2 3 2 × 3 = 6 4 - 6 1 5 1 × 5 = 5 6 - 8 5 7 5 × 7 = 35 8 - 10 6 9 6 × 9 = 54 10 - 12 2 11 2 ×11 = 22 12 - 14 3 13 3 × 13 = 39 Total 20 162

From the table, it can be observed that

Mean,

Therefore, mean number of plants per house is 8.1.

Here, direct method has been used as the values of class marks (xi) and fi are small.

Q2 :

Consider the following distribution of daily wages of 50 worker of a factory.

 Daily wages (in Rs) 100 - 120 120 - 140 140 - 1 60 160 - 180 180 - 200 Number of workers 12 14 8 6 10

Find the mean daily wages of the workers of the factory by using an appropriate method.

To find the class mark for each interval, the following relation is used.

Class size (h) of this data = 20

Taking 150 as assured mean (a), di, ui, and fiui can be calculated as follows.

 Daily wages (in Rs) Number of workers (fi) xi di = xi - 150 fiui 100 - 120 12 110 - 40 - 2 - 24 120 - 140 14 130 - 20 - 1 - 14 140 - 160 8 150 0 0 0 160 - 180 6 170 20 1 6 180 - 200 10 190 40 2 20 Total 50 - 12

From the table, it can be observed that

Therefore, the mean daily wage of the workers of the factory is Rs 145.20.

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 f.

 Daily pocket allowance (in Rs) 11 - 13 13 - 15 15 - 17 17 - 19 19 - 21 21 - 23 23 - 25 Number of workers 7 6 9 13 f 5 4

Q4 :

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Fine the mean heart beats per minute for these women, choosing a suitable method.

 Number of heart beats per minute 65 - 68 68 - 71 71 - 74 74 - 77 77 - 80 80 - 83 83 - 86 Number of women 2 4 3 8 7 4 2

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 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?

Q6 :

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.

Q7 :

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.

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.

 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

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 75 - 85 85 - 95 Number of cities 3 10 11 8 3

### Exercise 14.2 : Solutions of Questions on Page Number : 275

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 - 65 Number of patients 6 11 21 23 14 5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Q2 :

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

 Lifetimes (in hours) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Frequency 10 35 52 61 38 29

Determine the modal lifetimes of the components.

Q3 :

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

 Expenditure (in Rs) 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

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. Interpret the two measures.

 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

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 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

Find the mode of the data.

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 the mode of the data:

 Number 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

### Exercise 14.3 : Solutions of Questions on Page Number : 287

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 data and compare them.

 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

Q2 :

If the median of the distribution is given below is 28.5, find the values of x and y.

 Class interval Frequency 0 - 10 5 10 - 20 x 20 - 30 20 30 - 40 15 40 - 50 y 50 - 60 5 Total 60

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 to persons having age 18 years onwards but less than 60 year.

 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

Q4 :

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

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

Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5… 171.5 - 180.5)

Q5 :

Find the following table gives the distribution of the life time of 400 neon lamps:

 Life time (in hours) Number of lamps 1500 - 2000 14 2000 - 2500 56 2500 - 3000 60 3000 - 3500 86 3500 - 4000 74 4000 - 4500 62 4500 - 5000 48

Find the median life time of a lamp.

Q6 :

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

 Number of letters 1 - 4 4 - 7 7 - 10 10 - 13 13 - 16 16 - 19 Number of surnames 6 30 40 6 4 4

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Q7 :

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

 Weight (in kg) 40 - 45 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 Number of students 2 3 8 6 6 3 2

### Exercise 14.4 : Solutions of Questions on Page Number : 293

Q1 :

The following distribution gives the daily income of 50 workers of a factory.

 Daily income (in Rs) 100 - 120 120 - 140 140 - 160 160 - 180 180 - 200 Number of workers 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Q2 :

During the medical check-up of 35 students of a class, their weights were recorded as follows:

 Weight (in kg) Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.

Q3 :

The following table gives production yield per hectare of wheat of 100 farms of a village.

 Production yield (in kg/ha) 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Number of farms 2 8 12 24 38 16

Change the distribution to a more than type distribution and draw ogive.