NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.2

NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.2 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 14 Statistics Class 10 NCERT Solutions Ex 14.2.

BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 14
Chapter NameStatistics
ExerciseEx 14.2
Number of Questions Solved6
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.2

NCERT Solutions for Class 10 Maths

Question 1.
The following table shows the ages of the patients admitted in a hospital during a year:

Age (in years)5 – 1515 – 2525 – 3535 – 4545 – 5555 – 65
Number of patients6112123145

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Solution:
We may compute class marks (xi) as per the relation

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 1s
Now taking 30 as assumed mean (a) we may calculate di and fidi as following.

Age (in years)Number of patients
fi
class mark
xi
dixi – 30fidi
5 – 15610-20-120
15 – 251120-10-110
25 – 35213000
35 – 45234010230
45 – 55145020280
55 – 6556030150
Total80430

From the table we may observe that

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 1s.1
Clearly, mean of this data is 35.38. It represents that on an average the age of a patient admitted to hospital was 35.38 years.
As we may observe that maximum class frequency is 23 belonging to class interval 35 – 45.
So, modal class = 35 –  45
Lower limit (l) of modal class = 35
Frequency (f1) of modal class = 23
Class size (h) = 10
Frequency (f0) of class preceding the modal class = 21
Frequency (f2) of class succeeding the modal class = 14
NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 1s.2
Clearly mode is 36.8.It represents that maximum number of patients admitted in hospital were of 36.8 years.

Question 2.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours)0 – 2020 – 4040 – 6060 – 8080 – 100100 – 120
Frequency103552613829

Determine the modal lifetimes of the components.
Solution:
From the data given as above we may observe that maximum class frequency is 61 belonging to class interval 60 – 80.
So, modal class = 60 – 80
Lower class limit (l) of modal class = 60
Frequency (f1) of modal class = 61
Frequency (f0) of class preceding the modal class = 52
Frequency (f2) of class succeeding the modal class = 38
Class size (h) = 20
NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 2s
So, modal lifetime of electrical components is 65.625 hours.
Question 3.
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 – 150024
1500 – 200040
2000 – 250033
2500 – 300028
3000 – 350030
3500 – 400022
4000 – 450016
4500 – 50007

Solution:
We may observe from the given data that maximum class frequency is 40 belonging to 1500 – 2000 intervals.
So, modal class = 1500 – 2000
Lower limit (l) of modal class = 1500
Frequency (f1) of modal class = 40
Frequency (f0) of class preceding modal class = 24
Frequency (f2) of class succeeding modal class = 33
Class size (h) = 500

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 3s
Now we may find class mark as

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 3s.1
Class size (h) of give data = 500
Now taking 2750 as assumed mean (a) we may calculate di, ui and fiui as following

Expenditure 
(in Rs)
Number of familiesfixidi = xi – 2750NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 3s.2fiui
1000 – 1500241250-1500-3-72
1500 – 2000401750-1000-2-80
2000 – 2500332250-500-1-33
2500 – 3000282750000
3000 – 3500303250500130
3500 – 40002237501000244
4000 – 45001642501500348
4500 – 5000747502000428
Total200-35

Now from table may observe that
NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 3s.3
So, mean monthly expenditure was Rs.2662.50.

Question 4.
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 – 203
20 – 258
25 – 309
30 – 3510
35 – 403
40 – 450
45 – 500
50 – 552

Solution:
We may observe from the given data that maximum class frequency is 10 belonging to class interval 30 – 35.
So, modal class = 30 – 35
Class size (h) = 5
Lower limit (l) of modal class = 30
Frequency (f1) of modal class = 10
Frequency (f0) of class preceding modal class = 9
Frequency (f2) of class succeeding modal class = 3
NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 4s
It represents that most of states/U.T have a teacher  student ratio as 30.6

Now we may find class marks by using the relation

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 4s1
Now taking 32.5 as assumed mean (a) we may calculate di, ui and fiui as following.

Number of students
per teacher
Number of states/U.T
(fi)
 

xi

 

di = xi – 32.5

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 4s2 

fiui

15 – 20317.5-15-3-9
20 – 25822.5-10-2-16
25 – 30927.5-5-1-9
30 – 351032.5000
35 – 40337.5513
40 – 45042.51020
45 – 50047.51530
50 – 55252.52048
Total35-23

NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 4s3
So mean of data is 29.2
It represents that on an average teacher – student ratio was 29.2.

Question 5.
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Number of students
per teacher
Number of 
states/U.T
3000 – 40004
4000 – 500018
5000 – 60009
6000 – 70007
7000 – 80006
8000 – 90003
9000 -100001
10000 – 110001

Find the mode of the data.

Solution:
From the given data we may observe that maximum class frequency is 18 belonging to class interval 4000 – 5000.
So, modal class = 4000 – 5000
Lower limit (l) of modal class = 4000
Frequency (f1) of modal class = 18
Frequency (f0) of class preceding modal class = 4
Frequency (f2) of class succeeding modal class = 9
Class size (h) = 1000
NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 5s
So mode of given data is 4608.7 runs.

Question 6.
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 – 1010 – 2020 – 3030 – 4040 – 5050 – 660 – 7070 – 80
Frequency71413122011158

Solution:
From the given data we may observe that maximum class frequency is 20 belonging to 40 – 50 class intervals.
So, modal class = 40 – 50
Lower limit (l) of modal class = 40
Frequency (f1) of modal class = 20
Frequency (f0) of class preceding modal class = 12
Frequency (f2) of class succeeding modal class = 11
Class size = 10
NCERT Solutions for Class 10 Maths Chapter 14 Statistics ex 14.2 6s
So mode of this data is 44.7 cars.

 

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