RD Sharma Class 10 Solutions Chapter 7 Exercise 7.4 (Updated for 2021-22)

RD Sharma Class 10 Solutions Chapter 7 Exercise 7.4

RD Sharma Class 10 Solutions Chapter 7 Exercise 7.4: The median is the point in a distribution that is in the middle. Students will experience finding the median of a discrete and grouped frequency distribution in this exercise. The RD Sharma Class 10 Solutions is the best location to look for quick access to solutions. Download the RD Sharma Solutions for Class 10 Maths Chapter 7 Exercise 7.4 PDF for further details on this exercise.

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RD Sharma Class 10 Solutions Chapter 7 Exercise 7.4

Access answers to RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.4- Important Question with Answers

Question 1.
Following are the lives in hours of 15 pieces of the components of an aircraft engine. Find the median :
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719
Solution:
Arranging in ascending order, we get
694, 696, 699, 705, 710, 712, 715, 716, 719, 724, 725, 728, 729, 734, 745 Here N = 15 which is odd
RD Sharma Class 10 Chapter 7 Statistics

Question 2.
The following is the distribution of height of students of a certain class in a certain city :
Statistics Class 10 RD Sharma
Find the median height.
Solution:
Arranging the classes in exclusive form and then forming its cumulative frequency table as given
RD Sharma Class 10 Chapter 7 Statistics

Question 3.
Following is the distribution of I.Q. of 100 students. Find the median I.Q.
Statistics Class 10 RD Sharma
Solution:
Arranging the classes in exclusive form and then forming it in cumulative frequency table as shown below :
RD Sharma Class 10 Solutions Statistics
Here N = 100
∴ N2 = 1002 = 50
∴ Corresponding median class is = 94.5-104.5
l = 94.5, f= 33, F = 34 and h = 10
RD Sharma Class 10 Solutions Chapter 7 Statistics

Question 4.
Calculate the median from the following data :
RD Sharma Class 10 Solutions Statistics
Solution:
Writing the given data in a cumulative frequency table as shown
RD Sharma Class 10 Solutions Chapter 7 Statistics

Question 5.
Calculate the median from the following data :
RD Sharma Class 10 Pdf Chapter 7 Statistics
Solution:
RD Sharma Solutions Class 10 Chapter 7 Statistics

Question 6.
Calculate the missing frequency from the following distribution, it is given that the median of the distribution
RD Sharma Class 10 Pdf Chapter 7 Statistics
Solution:
Median = 24, let p be the missing frequency.
RD Sharma Solutions Class 10 Chapter 7 Statistics

Question 7.
The following table gives the frequency distribution of married women by age at marriage:
Learncbse.In Class 10 Chapter 7 Statistics
Calculate the median and interpret the results.
Solution:
Writing classes in exclusive form,
Class 10 RD Sharma Solutions Chapter 7 Statistics

Question 8.
The following table gives the distribution of the lifetime of 400 neon lamps :
Learncbse.In Class 10 Chapter 7 Statistics
Find the median life.
Solution:
Class 10 RD Sharma Solutions Chapter 7 Statistics
= 3000 + 406.98 = 3406.98

Question 9.
The distribution below gives the weight of 30 students in a class. Find the median weight of students :
RD Sharma Class 10 Pdf Free Download Full Book Chapter 7 Statistics
Solution:
Here N =30 ,N2 = 302 which lies in the class 55 – 60 ( ∵ 13 < 15 < 19)
RD Sharma Class 10 Solution Chapter 7 Statistics

Question 10.
Find the missing frequencies and the median for the following distribution if the mean is 1.46.
RD Sharma Class 10 Pdf Free Download Full Book Chapter 7 Statistics
Solution:
Mean = 1.46, N= 200
Let p1 and p2 be the missing frequencies
RD Sharma Class 10 Solution Chapter 7 Statistics
⇒ p1+ 2p2= 292 – 140 = 152
114-p2 + 2p2= 152
⇒ p2 = 152- 114 = 38
∴ p1= 114-p2= 114-38 = 76
Hence missing frequencies are 76 and 38
Median = Here N2 = 2002 = 100
∴ cf of 2nd class is 46 + 76 = 122
∴ Median = 1

Question 11.
An incomplete distribution is given below :
RD Sharma Class 10 Pdf Ebook Chapter 7 Statistics
You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
Solution:
Let p1, and p2 be the missing frequencies
Median = 46 and N = 230
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 7 Statistics
∴ 150 + p1 + p2 = 230

⇒ p1+p2 = 230 – 150 = 80
∴ p2 = 80-p1 ….(i)
∵ Median = 46 which lies in the class 40-50
∴ I = 40, f= 65, F = 42 +p1, h = 10
RD Sharma Class 10 Pdf Ebook Chapter 7 Statistics
⇒ 39 = 73 – p1
⇒ p1 = 73 -39 = 34
∴ p2 – 80 – p1 = 80 – 34 = 46
Hence missing frequencies are 34, and 46
Mean Let assumed mean (A) = 45
RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics
= 45 + 0.8695
= 45 + 0.87
= 45.87

Question 12.
If the median of the following frequency distribution is 28.5 find the missing frequencies:
Class 10 RD Sharma Chapter 7 Statistics
Solution:
Mean = 28.5 , N = 60
RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics
17 = 25 -f1
⇒ f1= 25 -17 = 8
and f2 = 15-f1 = 15-8 = 7
Hence missing frequencies are 8 and 7

Question 13.
The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:
RD Sharma Maths Class 10 Solutions Chapter 7 Statistics
Solution:
Median = 525, N = 100
RD Sharma Maths Class 10 Solutions Chapter 7 Statistics
⇒ 525 – 500 = (14 -f1) x 5
⇒ 25 = 70- 5f1
⇒ 5f1 = 70 – 25 = 45
⇒ f1 = 455 = 9
and f2 = 24 – f1 = 24 – 9 = 15
Hence f1 = 9, f2 = 15

Question 14.
If the median of the following data is 32.5, find the missing frequencies.
RD Sharma 10 Class Solutions Chapter 7 Statistics
Solution:
Mean = 32.5 and N= 40
RD Sharma 10 Class Solutions Chapter 7 Statistics
⇒ 2.5 x 12 = 60 – 10f1
⇒ 30 = 60 – 10f1
⇒ 10f1 = 60-30 = 30
⇒ f1 = 3010 =3
∴ f2 = 9 – f1 = 9-3 = 6
Hence f1 = 3, f2= 6

Question 15.
Compute the median for each of the following data:
RD Sharma Class 10 Textbook PDF Chapter 7 Statistics
Solution:
(i) Less than
Maths RD Sharma Class 10 Solutions Chapter 7 Statistics
Here N= 100=
∴ N2 = 1002 = 50 which lies in the class 70-90 (∵ 50 < 65 and > 43)
∴ l = 70, F =43 , f = 22 ,h = 20
RD Sharma Class 10 Textbook PDF Chapter 7 Statistics
(ii) Greater than
Maths RD Sharma Class 10 Solutions Chapter 7 Statistics
N = 150, N2 = 1502 = 75 which lies in the class 110-120 (∵ 75 > 105 and 75 > 60)
∴ l = 110, F = 60 , f=45, h= 10
RD Sharma Class 10 Textbook PDF Chapter 7 Statistics

Question 16.
A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and
the following data was obtained.
Maths RD Sharma Class 10 Solutions Chapter 7 Statistics
Find the median height.
Solution:
10th Maths Solution Book Pdf Chapter 7 Statistics
Here N2 = 512 = 25.5 or 26 which lies in the class 145-150
l= 145, F= 11, f= 18, h= 5
RD Sharma 10 Chapter 7 Statistics
= 145 + 4.03 = 149.03

Question 17.
A life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if policies are only given to persons having age 18 years onward but less than 60 years.
10th Maths Solution Book Pdf Chapter 7 Statistics
Solution:
RD Sharma 10 Chapter 7 Statistics
Here N = 100, N2 = 1002 = 50 which lies in the class 35-40 ( ∵ 45 > 50> 78)
l = 35, F = 45, f= 33, h = 5
RD Sharma 10 Chapter 7 Statistics
= 35 + 0.76 = 35.76

Question 18.
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:
RD Sharma Class 10 Book Pdf Chapter 7 Statistics
Find the mean length of the leaf.
Solution:
Solution Of RD Sharma Class 10 Chapter 7 Statistics
N = 40, N2 = 402 = 20 which lies in the class 144.5-153.5 as 17 < 20 < 29
∴ l= 144.5, F= 17, f= 12, h = 9
RD Sharma Class 10 Book Pdf Chapter 7 Statistics
= 144.5 + 2.25 = 146.75

Question 19.
An incomplete distribution is given as follows :
RD Sharma 10 Solutions Chapter 7 Statistics
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
Solution:
Median = 25 and ∑f= N = 170
Let p1 and p2 be two missing frequencies
RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.4 19a
∴ 110 + p1 +p2 = 170
⇒ p1+ p2 = 170 – 110 = 60
Here N = 170, N2 = 1702 = 85
∴ Median = 35 which lies in the class 30-40
Here l = 30, f= 40, F = 30 + p1 and h = 10
RD Sharma 10 Solutions Chapter 7 Statistics
20 = 55 – p1
⇒ p1 = 55 – 20 = 35
But p1+ p2 = 60
∴ p2 = 60 -p1 = 60 – 35 = 25
Hence missing frequencies are 35 and 25

Question 20.
The median of the distribution given below is 14.4. Find the values of x and y, if the total frequency is 20.
RD Sharma Maths Book For Class 10 Solution Chapter 7 Statistics
Solution:
RD Sharma Maths Book For Class 10 Solution Chapter 7 Statistics
It is given that n = 20
So, 10 + x + y – 20, i.e., x+y= 10 …(i)
It is also given that median = 14.4
Which lies in the class interval 12-18
So, l = 12, f= 5, cf = 4 + x, h = 6
Using the formula,
RD Sharma Class 10 Maths Chapter 7 Statistics

Question 21.
The median of the following data is SO. Find the values of p and q, if the sum of all the frequencies is 90.
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 7 Statistics
Solution:
RD Sharma Class 10 Maths Chapter 7 Statistics
Given, N = 90
∴ N2 = 902 = 45
Which lies in the interval 50-60
Lower limit, l = 50, f= 20, cf= 40 + p, h = 10
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 7 Statistics
∴ P = 5
Also, 78 +p + q = 90
⇒ 78 + 5 + q = 90
⇒ q = 90-83
∴ q = 7

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