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RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 9 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 24 - Measures of Central Tendency.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 9 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 9 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency Page/Excercise 24.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7


Solution 8


Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

(i)



(ii)

Solution 22


Solution 23

Solution 24

RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency Page/Excercise 24.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

x f xf
10 17 170
30 f1 30f1
50 32 1600
70 f2 70f2
90 19 1710
  N = 120


RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency Page/Excercise 24.3

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9


Solution 10

Solution 11

Solution 12

Solution 13


RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency Page/Excercise 24.4

Solution 1

Solution 2

Solution 3

Solution 4(i)

Arranging the data in an ascending order  14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28   Here observation 14 is having the highest frequency i.e. 4 in given data. So, mode of given data is 14.  

Solution 4 (ii)

Solution 5


RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency Page/Excercise 24.21

Solution 1

Range is not a measure of central value.

The difference between the highest value and the lowest value in the data set is called Range.

Hence, correct option is (b).

Solution 2

begin mathsize 12px style Mean space equals space straight X with bar on top space equals space fraction numerator Sum space of space all space observations over denominator Total space number space of space observations end fraction equals fraction numerator Sum space of space all space observations over denominator straight n end fraction
Now space if space straight k space is space added space to space each space observation
New space mean comma space stack straight X apostrophe with bar on top space equals space fraction numerator Sum space of space all space observations space plus space nk over denominator straight n end fraction equals fraction numerator Sum space of space all space observations over denominator straight n end fraction plus straight k
rightwards double arrow stack straight X apostrophe with bar on top equals straight X with bar on top space plus space straight k
Hence comma space correct space option space is space left parenthesis straight b right parenthesis. end style

RD Sharma Solution for Class 9 Mathematics Chapter 24 - Measures of Central Tendency Page/Excercise 24.22

Solution 3

begin mathsize 12px style Mean comma space straight X with bar on top space equals space fraction numerator Sum space of space all space observations over denominator Total space number space of space observations end fraction equals fraction numerator Sum space of space all space observations over denominator straight n end fraction
If space each space observation space is space multiplied space by space straight k comma space then space
New space mean comma space stack straight X apostrophe with bar on top space equals space fraction numerator open parentheses Sum space of space all space observations close parentheses space straight k over denominator straight n end fraction
rightwards double arrow stack straight X apostrophe with bar on top space equals straight k straight X with bar on top
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end style

Solution 4

begin mathsize 12px style Mean space equals space 81 space equals space fraction numerator Sum space of space Seven space numbers over denominator 7 end fraction
rightwards double arrow Sum space of space Seven space numbers space equals space 81 space cross times space 7 space equals space 567
Let space the space discarded space number space be space straight x.
rightwards double arrow Sum space of space 6 space numbers space equals space 567 minus straight x
Now comma space mean space of space remaining space 6 space numbers space space equals space fraction numerator 567 minus straight x over denominator 6 end fraction equals 78
rightwards double arrow 567 space minus space straight x space equals space 468
rightwards double arrow straight x space equals space 99
So comma space discarded space number space is space 99.
Hence comma space correct space option space is space left parenthesis straight b right parenthesis. end style

Solution 5

 

  Mean Median Mode
2, 2, 2, 2, 4 12/5 = 2.4  2 2
1, 3, 3, 3, 5 15/5 = 3 3 3
1, 1, 2, 5, 6 15/5 = 3 2 1
1, 1, 1, 2, 5 10/5 = 2 1 1

From above table, data 1, 3, 3, 3, 5 has mean, median, mode all have same value, i.e. 3.

Hence, correct option is (b).

Solution 6

begin mathsize 12px style 2 comma space 2 comma space 4 comma space 5 comma space 12
Median space equals space 4
Mode space equals space 2
Mean space equals space fraction numerator 2 plus 2 plus 4 plus 5 plus 12 over denominator 5 end fraction equals 25 over 5 equals 5
Hence space left parenthesis Mean space equals space 5 right parenthesis space greater than space left parenthesis Mode space equals space 2 right parenthesis
Hence comma space c orrect space option space is space left parenthesis straight b right parenthesis. end style

Solution 7

begin mathsize 12px style Mean space equals space fraction numerator 7 plus 5 plus 13 plus straight x plus 9 over denominator 5 end fraction equals 10
rightwards double arrow 34 space plus space straight x space equals space 50
rightwards double arrow straight x space equals space 16
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 8

begin mathsize 12px style Mean space of space first space five space observations space equals space fraction numerator straight x plus straight x plus 2 plus straight x plus 4 plus straight x plus 6 plus straight x plus 8 over denominator 5 end fraction equals 11
rightwards double arrow 5 straight x space plus space 20 space equals space 55
rightwards double arrow straight x space equals space 7
rightwards double arrow First space three space numbers space are space 7 comma space 9 comma space 11
Mean space equals space fraction numerator 7 plus 9 plus 11 over denominator 3 end fraction equals 27 over 3 equals space 9
Hence comma space correct space opion space is space left parenthesis straight a right parenthesis. end style

Solution 9

Most Frequent value is called mode.

Hence, correct option is (c).

Solution 10

begin mathsize 12px style In space data space 5 comma space 4 comma space 7 comma space 5 comma space 8 comma space 8 comma space 8 comma space 5 comma space 7 comma space 9 comma space 5 comma space 7 comma space 9 comma space 10 comma space 8 comma
We space observe space that space values space 5 space space and space 8 space both space have space maximum space frequency space straight i. straight e. space 4
So comma space 5 space and space 8 comma space both space are space mode space of space this space data. end style

Solution 11

begin mathsize 12px style Data colon space 0 comma space 2 comma space 2 comma space 2 comma space minus 3 comma space 5 comma space minus 1 comma space 5 comma space 5 comma space minus 3 comma space 6 comma space 6 comma space 5 comma space 6 space
Rearranging space data space in space increasing space order comma space we space have
minus 3 comma space minus 3 comma space minus 1 comma space 0 comma space 2 comma space 2 comma space 2 comma space 5 comma space 5 comma space 5 comma space 5 comma space 6 comma space 6 comma space 6
Number space of space observations space equals space straight n space equals space 14 space left parenthesis even right parenthesis
Now comma space median space equals space fraction numerator begin display style open parentheses straight n over 2 close parentheses to the power of th space observation plus space open parentheses fraction numerator straight n plus 1 over denominator 2 end fraction close parentheses to the power of th space observation end style over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 7 to the power of th space observation space plus space 8 to the power of th space observation over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 plus 5 over denominator 2 end fraction
rightwards double arrow Median space equals space 3.5
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 12

begin mathsize 12px style If space top enclose straight k space is space the space mean space of space straight n space observations space straight x subscript 1 comma space straight x subscript 2 comma space straight x subscript 3 comma space straight x subscript 4 space.... straight x subscript straight n.
then space algebraic space sum space of space deviations space equals space sum from straight i equals 0 to straight n of space open parentheses straight x subscript straight i space minus space top enclose straight x close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals sum from straight i equals 0 to straight n of space straight x subscript straight i space minus space straight n space top enclose straight x
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space straight n open parentheses fraction numerator sum from straight i equals 0 to straight n of space straight x subscript straight i over denominator straight n end fraction close parentheses space minus space straight n top enclose straight x space space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space straight n top enclose straight x space minus space straight n top enclose straight x
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end style

Solution 13

begin mathsize 12px style Arranging space data space in space ascending space order comma space we space have
straight A colon space 1 comma space 2 comma space 2 comma space 3 comma space 3 comma space 3 comma space 7
straight B colon space 3 comma space 5 comma space 5 comma space 7 comma space 8 comma space 9 comma space 12
straight C colon space 2 comma space 3 comma space 4 comma space 4 comma space 4 comma space 7 comma space 11
Mean space of space straight A space equals space fraction numerator 1 plus 2 plus 2 plus 3 plus 3 plus 3 plus 7 over denominator 7 end fraction equals 21 over 7 equals 3
Mean space of space straight B space equals space fraction numerator 3 plus 5 plus 5 plus 7 plus 8 plus 9 plus 12 over denominator 7 end fraction equals 49 over 7 equals 7
Mean space of space straight C space equals space fraction numerator 2 plus 3 plus 4 plus 4 plus 4 plus 7 plus 11 over denominator 7 end fraction equals 35 over 7 equals 5

Mode space of space straight A space equals space 3 space space space space space space space space space space space space space space space Median space of space straight A space equals space 3
Mode space of space straight B space equals space 5 space space space space space space space space space space space space space space space Median space of space straight B space space equals space 7
Mode space of space straight C space equals space 4 space space space space space space space space space space space space space space space Median space of space straight C space equals space 4

open parentheses Mean space of space straight A space equals space 3 close parentheses space not equal to space open parentheses Mode space of space straight C space equals space 4 close parentheses
open parentheses Mean space of space straight C space equals space 5 close parentheses space not equal to space left parenthesis Median space of space straight B space equals space 7 right parenthesis
open parentheses Median space of space straight B space equals 7 close parentheses space space not equal to space open parentheses Mode space of space straight A space equals space 3 close parentheses
Mean space of space straight A space equals space 3 comma space Mode space of space straight A space equals space 3 comma space Median space of space straight A space equals space 3
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 14

The empirical Relation between mean, median and mode is

Mode = 3 Median - 2 mean

Hence, correct option is (a).

Solution 15

begin mathsize 12px style Mean space equals space fraction numerator straight a plus straight b plus straight c plus straight d plus straight e over denominator 5 end fraction equals 28
rightwards double arrow straight a plus straight b plus straight c plus straight d plus straight e space equals space 140 space space space space space space space.... open parentheses 1 close parentheses
Also comma space Mean space equals space fraction numerator straight a plus straight c plus straight e over denominator 3 end fraction equals 24 space
rightwards double arrow straight a plus straight c plus straight e space equals 72 space space space space space space space space.... open parentheses 2 close parentheses
Subtracting space equation space open parentheses 2 close parentheses space from space open parentheses 1 close parentheses comma space we space have
straight b plus straight d space equals space 68
Mean space equals space fraction numerator straight b plus straight d over denominator 2 end fraction space equals space 68 over 2 equals 34
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 24 - Measures of Central Tendency for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 24 - Measures of Central Tendency.

Text Book Solutions

CBSE IX - Mathematics

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