Chapter 24 : Measures of Central Tendency - Rd Sharma Solutions for Class 9 Maths CBSE

If you love numbers & have a deep interest in statistics, then Mathematics is probably one of the scoring subject ever. A Class 9th CBSE Mathematics is one of the challenging subject one can undergo as, it involves a lot of crunching of complex numbers, geometrical formulae, diagrams & much more. Hence, to simplify the mathematical complexity, TopperLearning has framed a customise solution that involves Test preparation notes, Textbook solutions, Videos, & several other study material that help the student to memorise the concepts quickly. We have bifurcated our CBSE Class 9 Study Material (Solution) into 3 Different parts namely: 

- CBSE Class 9 Practice Test includes Revision notes, Question bank & Sample Paper 
- TopperLearning Classroom that includes Videos, Ask the Experts & Preparation Tips
- Text Book Solutions, etc

TopperLearning packages involves all the ingredients of CBSE Class 9 Study Material that includes Solved Question Papers, High Animated Videos, Solutions by SME (Subject Matter Expert), CBSE class 9 Preparation Tips, Update to CBSE 9th Mathematics syllabus, Practice books, Reference Materials, etc that help you to score great marks with glorious marks.

Getting a good score is now relatively easy if you prefer TopperLearning solutions for CBSE Class 9th Mathematics subject. By purchasing our package, you will be accessed to guaranteed success in your examination!

Read  more

Chapter 24 - Measures of Central Tendency Excercise Ex. 24.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Find the mean of first five multiples of 3.
Solution 7

Question 8
Solution 8

Question 9
Solution 9
Question 10

The numbers of children in 10 families of a locality are:

2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

The traffic police recorded the speed (in km/hr) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48. Later on an error in recording instrument was found. Find the correct average speed of the motorists if the instrument recorded 5 km/hr less in each case.

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

If M is the mean of x1, x2, x3, x4, x5 and x6 , prove that

(x1 - M) + (x2 - M) + (x3 -M) + (x4 - M) + (x- M) + (x6 - M) = 0

Solution 19

Question 20

Solution 20

Question 21

Solution 21
(i)



(ii)

Question 22
Solution 22

Question 23
Solution 23
Question 24
Solution 24

Chapter 24 - Measures of Central Tendency Excercise Ex. 24.2

Question 1
Solution 1

Question 2
Solution 2

Question 3

Solution 3

Question 4

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss No. of tosses
0

1

2

3

4

5

38

144

342

287

164

25
Total 1000



Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12
x f xf
10 17 170
30 f1 30f1
50 32 1600
70 f2 70f2
90 19 1710
  N = 120


Chapter 24 - Measures of Central Tendency Excercise Ex. 24.3

Question 1

Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Numbers 50, 42, 35, 2x + 10, 2x - 8, 12, 11, 8 are written in descending order and their median is 25, find x.
Solution 9

Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
    29,    32,    48,    50,    x,    x + 2,    72,    78,    84,    95    

Solution 13

Chapter 24 - Measures of Central Tendency Excercise Ex. 24.4

Question 1
Solution 1

Question 2
Solution 2

Question 3
Solution 3

Question 4
Find the mode of
        14,      25,    14,    28,    18,    17,    18,    14,    23,    22,    14,    18
Solution 4
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.  

Question 5
Solution 5

Question 6
The demand of different sizes, as obtained by a survey, is given below:

Size 38 39 40 41 42 43 44 Total
Number of persons (wearing it): 26 39 20 15 13 7 5 125

Find the modal shirt size, as observed from the survey.
Solution 6

Chapter 24 - Measures of Central Tendency Excercise 24.21

Question 1

Which one of the following is not a measure of central value?

(a) Mean

(b) Range

(c) Median

(d) Mode

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).

Question 2

begin mathsize 12px style The space mean space of space straight n space observations space is space straight X with bar on top. space If space straight k space is space added space to space each space observation comma space then space new space mean space is
left parenthesis straight a right parenthesis space straight X with bar on top
left parenthesis straight b right parenthesis space straight X with bar on top space plus space straight k
left parenthesis straight c right parenthesis space straight X with bar on top space minus space straight k
left parenthesis straight d right parenthesis space straight k straight X with bar on top end style

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

Chapter 24 - Measures of Central Tendency Excercise 24.22

Question 1

begin mathsize 12px style The space mean space of space straight n space observations space is space straight X with bar on top. space If space each space observation space is space multiplied space by space straight k comma space the space mean space of space new space observations space is
left parenthesis straight a right parenthesis space straight k straight X with bar on top
left parenthesis straight b right parenthesis space fraction numerator straight X with bar on top over denominator straight k end fraction
left parenthesis straight c right parenthesis space straight X with bar on top plus straight k
left parenthesis straight d right parenthesis space straight X with bar on top minus straight k end style

Solution 1

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

Question 2

The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value of discarded number is

(a) 98

(b) 99

(c) 100

(d) 101

Solution 2

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

Question 3

For which set of numbers do the mean, median and mode all have the same value?

(a) 2, 2, 2, 2, 4

(b) 1, 3, 3, 3, 5

(c) 1, 1, 2, 5, 6

(d) 1, 1, 1, 2, 5

Solution 3

 

  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).

Question 4

For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?

(a) Mean = Median

(b) Mean > Mode

(c) Mean < Mode

(d) Mode = Median

Solution 4

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

Question 5

If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value of x is

(a) 10

(b) 12

(c) 14

(d) 16

Solution 5

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

Question 6

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8, is 11, then the mean of first three observations is

(a) 9

(b) 11

(c) 13

(d) none of these

Solution 6

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

Question 7

Mode is

(a) least frequent value

(b) middle most value

(c) most frequent value

(d) none of these

Solution 7

Most Frequent value is called mode.

Hence, correct option is (c).

Question 8

The following is the data of wages per day: 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8

The mode of the data is

(a) 7

(b) 5

(c) 8

(d) 10

Solution 8

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

Question 9

The median of the following data: 0, 2, 2, 2, -3, 5, -1, 5, 5, -3, 6, 6, 5, 6 is

(a) 0

(b) -1.5

(c) 2

(d) 3.5

Solution 9

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

Question 10

The algebraic sum of the deviations of a set of n values from their mean is

(a) 0

(b) n - 1

(c) n

(d) n + 1

Solution 10

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

Question 11

A, B, C are three sets of values of x:

A: 2, 3, 7, 1, 3, 2, 3

B: 7, 5, 9, 12, 5, 3, 8

C: 4, 4, 11, 7, 2, 3, 4

Which one of the following statements is correct?

(a) Mean of A = Mode of C

(b) Mean of C = Median of B

(c) Median of B = Mode of A

(d) Mean, Median and Mode of A are equal.

Solution 11

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

Question 12

The empirical relation between mean, mode and median is

(a) Mode = 3 Median - 2 Mean

(b) Mode = 2 Median - 3 Mean

(c) Median = 3 Mode - 2 Mean

(d) Mean = 3 Median - 2 Mode

Solution 12

The empirical Relation between mean, median and mode is

Mode = 3 Median - 2 mean

Hence, correct option is (a).

Question 13

The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, what is the mean of b and d?

(a) 31

(b) 32

(c) 33

(d) 34

Solution 13

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

CBSE Class 9 Maths Homework Help

Clear all your doubts instantly at our “Ask Doubt” section. Get expert help and guidance at your comfort. To know the syllabus in detail, click here.

 

NCERT Textbooks are the rich stimulant for those students who want to score better in the CBSE examinations. By solving our papers the students have achieved a better and higher result. One of the primary objectives of creating ncert solution for class 9  is that the student gets access to an easy solution; which acts as a strong catalyst in improving the marks. We usually focus that the students don’t find any difficulty in understanding the concepts and can memorize them easily.