Ncert Solutions For Class 9 Maths Ex 14.2

Ncert Solutions For Class 9 Maths Chapter 14 Ex 14.2

 

Q1)The blood group record of 30 pupil of standard 9th are recorded in a following data:

A, O, AB, B, O, O, O, A, B, B, O, A, O, A, O

AB, A, O, O, A, O, A, AB, B, O, A, A, B, O, B

Illustrate this report in a form of a frequency distribution table.

Give the rarest blood group of these pupil present In the classroom.

Solution:

The frequency refers to the number of students having same blood group. We will represent the data in table:

Blood Group Number of Students

(Frequency)

A 9
B 6
O 12
AB 3
Total 30

 

Most common Blood Group (Highest frequency): O
Rarest Blood Group (Lowest frequency): AB

 

Q2)  The range in km of 40 doctors from their residences to their offices were found as follows:

19    10    12    17    18    11    32    17    16    2
5       3     10    20     25     11   13    7      12    31

12    14    2    9    6    15    15    7    6    12
7        9    7    8    3    5    12    15   18    3

Create a grouped frequency table with class size 5 for the data given above by taking an interval of 0-5 (5 not included). What are the important features do you get from the table representation?

Solution:

The given data is very large. So, we construct a group frequency of class size 5. Therefore, class interval will be 0-5, 5-10, 10-15, 15-20 and so on. The data is represented in the table as:

2
The classes in the table are not overlapping. Also, 36 out of 40 engineers have their house below 20 km of distance.

 

Q3) The absolute moisture content (in %) of a certain place for a month of thirty days was as follows:


98.1     92.3     99.2     90.2     86.5     98.3     97.3      93.3      92.1      89
89.2     92.1     97.1     90.3     92.7     95.3     92.9      96.1      94.2      95.1
96.2     98.6     84.9     93.5     95.7     95.1     97.2      96.3      95.2      97.3


(i) table the given distribution value of 84 – 86, 86 – 88, etc.
(ii) Give the month or session in which the data is constructed.
(iii) Find the range of the given data.

Solution:

(i) The given data is very large. So, we construct a group frequency of class size 2. Therefore, class interval will be 84-86, 86-88, 88-90, 90-92 and so on. The data is represented in the table as:

Relative humidity (in %) Frequency
84-86 1
86-88 1
88-90 2
90-92 2
92-94 7
94-96 6
96-98 7
98-100 4
Total 30

(ii) The moisture content is very high in the data which is observed during rainy season. So, it must be rainy season.
(iii) Range of data = Maximum value of data – Minimum value of data = 99.2 – 84.9 = 14.3

Q4) The length of pants of fifty students, measured in centimeters, have been found to be as follows:


161     159     162     165     158     161     158     162     160     164
162     152     153     165     168     154     160     172     150     151
153     164     171     170     168     165     154     168     154     170
154     159     161     156     158     162     156     161     165     159
161     150     154     167     162     159     166     153     173     166


(i) Illustrate the given data by the grouped frequency distribution table, taking the class intervals as 160 – 165, 165 – 170, etc.
(ii) What can be summarized about their heights from the table?

Solution:

The data with class interval 160-165, 165-170 and so on is represented in the table as:

Height (in cm) No. of Students
(Frequency)
150-155 12
155-160 9
160-165 14
165-170 10
170-175 5
Total 50

(ii) From the given data, it can be concluded that 35 students i.e. more than 50% are shorter than 165 cm.

Q5)A survey was done to check the concentration of carbon dioxide in the atmosphere in parts per million (ppm) of a particular city. The metadata observed for 30 days is as follows:


0.03     0.07     0.08     0.09     0.04     0.17
0.16     0.01     0.02     0.06     0.18     0.20
0.11     0.05     0.12      0.13      0.22     0.07
0.08   0.08     0.10     0.06     0.09     0.18
0.11    0.08     0.05     0.07     0.01     0.04


(i) Construct a grouped frequency distribution table for the meta data with intervals as 0.00 – 0.04, 0.04 – 0.08, and so on.
(ii) For how many days, was the concentration of carbon dioxide more than 0.11 ppm?

Solution:

The data with class interval 0.00 – 0.04, 0.04 – 0.08 and so on is represented in the table as:

 

Concentration of carbon dioxide in air(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
Total 30

 

(ii) 2 + 4 + 2 = 8 days have the concentration of carbon dioxide more than 0.11 parts per million.

Q6)  3 coins were flipped thirty times simultaneously. Every time the number of heads occurring was written down as follows:


3     0     2     1     3     2     1     0     3     1
0     1     1     2     2     2     0     1     2     1
1     3     0     2     1     1     3     0     2     2


Construct a frequency distribution table for the values given above.

Solution:

The frequency distribution table for the data given above can be prepared as follow:

Number of Heads Frequency
0 6
1 10
2 9
3 5
Total 30

 

Q7) The value of pie upto 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510
(i) Construct a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii) What are the maximum and the minimum frequently occurring digits?

Solution:

The frequency is given as follow:

Digits Frequency
0 2
1 5
2 5
3 8
4 4
5 5
6 4
7 4
8 5
9 8
Total 30

(ii) The digit having the least frequency occurs the least and the digit with highest frequency occurs the most. 0 has frequency 2 and thus occurs least frequently while 3 and 9 have frequency 8 and thus occurs most frequently.

Q8)There are 30 men who were questioned about the number of hours they spend in office in the previous week. The results were found as follows:


1     6     2     3     5    12     5     8     4     8
10   3     4     12   2     8     15    1     17   6
3     2     8     5     9     6      8     7     14   12


(i) Make a grouped frequency distribution table for this data, taking a class width of 5 and one of the class intervals as 5-10.
(ii) How many men spend 15 or more hours a week?

Solution:

The distribution table for the given data, taking class width 5 and one of the class intervals as 5-10 is as follows:

Number of Hours Frequency
0-5 10
5-10 13
10-15 5
15-20 2
Total 30

(ii) We observed from the given table that 2 children television for 15 or more hours a week.

Q9)A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:


2.6     3.0    3.7     3.2     2.2     4.1     3.5     4.5
3.5     2.3    3.2     3.4     3.8     3.2     4.6     3.7
2.5     4.4    3.4     3.3     2.9     3.0     4.3     2.8
3.5     3.2    3.9     3.2     3.2     3.1     3.7     3.4
4.6     3.8    3.2     2.6     3.5     4.2     2.9     3.6


Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.

Solution:

A grouped frequency distribution table using class intervals of size 0.5 starting from the interval 2 – 2.5 is constructed.

Lives of batteries (in years) No. of batteries
(Frequency)
2-2.5 2
2.5-3 6
3-3.5 14
3.5-4 11
4-4.5 4
4.5-5 3
Total 40