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# RD Sharma solutions for Mathematics for Class 9 chapter 24 - Measures of Central Tendency [Latest edition]

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## Chapter 24: Measures of Central Tendency

Ex. 24.1Ex. 24.2Ex. 24.3Ex. 24.4Others

#### RD Sharma solutions for Mathematics for Class 9 Chapter 24 Measures of Central TendencyExercise 24.1 [Pages 9 - 10]

Ex. 24.1 | Q 1 | Page 9

If the heights of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively,
find the mean height.

Ex. 24.1 | Q 2 | Page 9

Find the mean of 994, 996, 998, 1002 and 1000.

Ex. 24.1 | Q 3 | Page 9

Find the mean of first five natural numbers .

Ex. 24.1 | Q 4 | Page 9

Find the mean of all factors of 10.

Ex. 24.1 | Q 5 | Page 9

Find the mean of first 10 even natural numbers.

Ex. 24.1 | Q 6 | Page 9

Find the mean of x, x + 2, x + 4, x +6, x + 8.

Ex. 24.1 | Q 7 | Page 9

Find the mean of first five multiples of 3.

Ex. 24.1 | Q 8 | Page 9

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:
3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean   x.

Ex. 24.1 | Q 9 | Page 9

The percentage of marks obtained by students of a class in mathematics are : 64, 36, 47, 23,
0, 19, 81, 93, 72, 35, 3, 1. Find their mean.

Ex. 24.1 | Q 10 | Page 9

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.

Ex. 24.1 | Q 11 | Page 9

Explain, by taking a suitable example, how the arithmetic mean alters by

(i) adding a constant k to each term

(ii) subtracting a constant k from each them

(iii) multiplying each term by a constant k and

(iv) dividing each term by a non-zero constant k.

Ex. 24.1 | Q 12 | Page 9

The mean of marks scored by 100 students was found to be 40. Later on it was discovered
that a score of 53 was misread as 83. Find the correct mean.

Ex. 24.1 | Q 13 | Page 9

The traffic police recorded the speed (in kmlhr) 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 overagespeed of the motorists if the instrument recorded 5 km/hr less in each case.

Ex. 24.1 | Q 14 | Page 9

The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the
excluded number.

Ex. 24.1 | Q 15 | Page 9

The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6
of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.

Ex. 24.1 | Q 16 | Page 10

The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?

Ex. 24.1 | Q 17 | Page 10

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

Ex. 24.1 | Q 18 | Page 10

The mean of 200 items was 50. Later on, it was discovered that the two items were misread
as 92 and 8 instead of 192 and 88. Find the correct mean.

Ex. 24.1 | Q 19 | Page 10

If M is the mean of x1 , x2 , x3 , x4 , x5 and x6, prove that
(x1 − M) + (x2 − M) + (x3 − M) + (x4 − M) + (x5 — M) + (x6 − M) = 0.

Ex. 24.1 | Q 20 | Page 10

Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by
the Meteorological Department are given below: 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9

(i) Find the mean 𝑋 ̅
(ii) Verify that = sum _ ( i = 1)^10(xi - x ) = 0

Ex. 24.1 | Q 21 | Page 10

Find the values of n and X in each of the following cases :

(i)  sum _(i = 1)^n(xi - 12) = - 10 sum _(i = 1)^n(xi - 3) = 62

(ii) sum _(i = 1)^n (xi - 10) = 30  sum _(i = 6)^n (xi - 6) = 150 .

Ex. 24.1 | Q 22 | Page 10

The sums of the deviations of a set of n values 𝑥1, 𝑥2, … . 𝑥11 measured from 15 and −3 are − 90 and 54 respectively. Find the valùe of n and mean.

Ex. 24.1 | Q 23 | Page 10

Find the sum of the deviations of the variate values 3, 4, 6, 7, 8, 14 from their mean.

Ex. 24.1 | Q 24 | Page 10

If x is the mean of the ten natural numbers x_1, x_2 , x_3+....... + x_10 show that (x1 -x) + (x2 - x) +.........+ (x10 - x) = 0

#### RD Sharma solutions for Mathematics for Class 9 Chapter 24 Measures of Central TendencyExercise 24.2 [Pages 14 - 16]

Ex. 24.2 | Q 1 | Page 14

Calculate the mean for the following distribution:

 x : 5 6 7 8 9 f : 4 8 14 11 3
Ex. 24.2 | Q 2 | Page 14

Find the mean of the following data:

 x : 19 21 23 25 27 29 31 f : 13 15 16 18 16 15 13

Ex. 24.2 | Q 3 | Page 14

Find the mean of the following distribution:

 x : 10 12 20 25 35 F : 3 10 15 7 5
Ex. 24.2 | Q 4 | Page 15

Five coins were simultaneously tossed 1000 times and at each toss the number of heads wereobserved. 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 38 1 144 2 342 3 287 4 164 5 25 TOtal 1000

Ex. 24.2 | Q 5 | Page 15

The mean of the following data is 20.6. Find the value of p.

 x : 10 15 p 25 35 f : 3 10 25 7 5
Ex. 24.2 | Q 6 | Page 15

If the mean of the following data is 15, find p.

 x: 5 10 15 20 25 f : 6 p 6 10 5
Ex. 24.2 | Q 7 | Page 15

Find the value of p for the following distribution whose mean is 16.6

 x: 8 12 15 p 20 25 30 f : 12 16 20 24 16 8 4
Ex. 24.2 | Q 8 | Page 15

Find the missing value of p for the following distribution whose mean is 12.58.

 x 5 8 10 12 p 20 25 f 2 5 8 22 7 4 2
Ex. 24.2 | Q 9 | Page 15

Find the missing frequency (p) for the following distribution whose mean is 7.68.

 x 3 5 7 9 11 13 f 6 8 15 p 8 4
Ex. 24.2 | Q 10 | Page 15

Find the value of p, if the mean of the following distribution is 20.

 x: 15 17 19 20+p 23 f: 2 3 4 5p 6
Ex. 24.2 | Q 11 | Page 15

Candidates of four schools appear in a mathematics test. The data were as follows:

 Schools No. of candidates Average score 1 60 75 2 48 80 3 N A 55 4 40 50

If the average score of the candidates of all the four schools is 66, find the number of
candidates that appeared from school 3.

Ex. 24.2 | Q 12 | Page 16

Find the missing frequencies in the following frequency distribution if its known that the mean of the distribution is 50.

 x 10 30 50 70 90 f 17 f1 32 f2 19 Total =120

#### RD Sharma solutions for Mathematics for Class 9 Chapter 24 Measures of Central TendencyExercise 24.3 [Page 18]

Ex. 24.3 | Q 1 | Page 18

Find the median of the following data (1-8)

83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Ex. 24.3 | Q 2 | Page 18

Find the median of the following data (1-8)

133, 73, 89, 108, 94, 1O4, 94, 85, 100, 120

Ex. 24.3 | Q 3 | Page 18

Find the median of the following data (1-8)

31 , 38, 27, 28, 36, 25, 35, 40

Ex. 24.3 | Q 4 | Page 18

Find the median of the following data (1-8)

15, 6, 16, 8, 22, 21, 9, 18, 25

Ex. 24.3 | Q 5 | Page 18

Find the median of the following data (1-8)

41, 43, 127, 99, 71, 92, 71, 58, 57

Ex. 24.3 | Q 6 | Page 18

Find the median of the following data (1-8)

25, 34, 31, 23, 22, 26, 35, 29, 20, 32

Ex. 24.3 | Q 7 | Page 18

Find the median of the following data (1-8)

12, 17, 3, 14, 5, 8, 7, 15

Ex. 24.3 | Q 8 | Page 18

Find the median of the following data (1-8)

92, 35, 67, 85, 72, 81, 56, 51, 42, 69

Ex. 24.3 | Q 9 | Page 18

Numbers 50, 42, 35, 2x + 10, 2x − 8, 12, 11, 8 are written in descending order and their
median is 25, find x.

Ex. 24.3 | Q 10 | Page 18

Find the median of the following observations : 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

Ex. 24.3 | Q 11 | Page 18

Find the median of the following data : 41, 43, 127, 99, 61, 92, 71, 58, 57 If 58 is replaced
by 85, what will be the new median.

Ex. 24.3 | Q 12 | Page 18

The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42,30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.

Ex. 24.3 | Q 13 | Page 18

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

#### RD Sharma solutions for Mathematics for Class 9 Chapter 24 Measures of Central TendencyExercise 24.4 [Page 20]

Ex. 24.4 | Q 1 | Page 20

Find out the mode of the following marks obtained by 15 students in a class:
Marks : 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7, 7.

Ex. 24.4 | Q 2 | Page 20

Find the mode from the following data:

125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125

Ex. 24.4 | Q 3 | Page 20

Find the mode for the following series :
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7,7.5, 7.3, 7.2, 7.6, 7.2

Ex. 24.4 | Q 4.1 | Page 20

Find the mode of the following data :
14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18

Ex. 24.4 | Q 4.2 | Page 20

Find the mode of the following data :
7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7

Ex. 24.4 | Q 5 | Page 20

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

 Size: 38 39 40 41 42 43 44 Total No of persons(wearing it) 26 39 20 15 13 7 5 125

Find the modal shirt sizes, as observed from the survey.

#### RD Sharma solutions for Mathematics for Class 9 Chapter 24 Measures of Central Tendency [Page 21]

Q 1 | Page 21

If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.

Q 2 | Page 21

If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.

Q 3 | Page 21

If the median of scores $\frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5}$  and $\frac{x}{6}$  (where x > 0) is 6, then find the value of $\frac{x}{6}$ .

Q 4 | Page 21

If the mean of 2, 4, 6, 8, xy is 5, then find the value of x + y.

Q 5 | Page 21

If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.

Q 6 | Page 21

If the median of 33, 28, 20, 25, 34, x is 29, find the maximum possible value of x.

Q 7 | Page 21

If the median of the scores 1, 2, x, 4, 5 (where 1 < 2 < x < 4 < 5) is 3, then find the mean of the scores.

Q 8 | Page 21

If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean

Q 9 | Page 21

The arithmetic mean and mode of a data are 24 and 12 respectively, then find the median of the data.

Q 10 | Page 21

If the difference of mode and median of a data is 24, then find the difference of median and mean.

#### RD Sharma solutions for Mathematics for Class 9 Chapter 24 Measures of Central Tendency [Pages 21 - 22]

Q 1 | Page 21

Mark the correct alternative in each of the following:
Which one of the following is not a measure of central value?

• Mean

• Range

• Median

• Mode

Q 2 | Page 21

The mean of n observations is X. If k is added to each observation, then the new mean is

• X

•  X + k

•  X − k

• kX

Q 3 | Page 22

The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is

• k bar(X) 

• bar(X)/k

• bar(X)  +k

• bar(X)- k`

Q 4 | Page 22

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

• 98

• 99

•  100

•  101

Q 5 | Page 22

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

• 2, 2, 2, 2, 4

•  1, 3, 3, 3, 5

• 1, 1, 2, 5, 6

•  1, 1, 1, 2, 5

Q 6 | Page 22

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

• Mean = Median

• Mean > Mode

•  Mean > Mode

• Mode = Median

Q 7 | Page 22

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

• 10

• 12

• 14

• 16

Q 8 | Page 22

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

• 9

• 11

• 13

• none of these

Q 9 | Page 22

Mode is

• least frequent value

•  middle most value

• most frequent value

•  none of these

Q 10 | Page 22

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

• 7

• 5

• 8

• 10

Q 11 | Page 22

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

• 0

•  −1.5

• 2

• 3.5

Q 12 | Page 22

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

• 0

• n − 1

•  n

• n + 1

Q 13 | Page 22

A, B, C are three sets of values of x

(a) 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?

• Mean of A = Mode of C

•  Mean of C = Median of B

•  Median of B = Mode of A

• Mean, Median and Mode of A are equal.

Q 14 | Page 22

The empirical relation between mean, mode and median is

• Mode = 3 Median − 2 Mean

• Mode = 2 Median − 3 Mean

• Median = 3 Mode − 2 Mean

•  Mean = 3 Median − 2 Mode

Q 15 | Page 22

The mean of abcd and e is 28. If the mean of ac, and e is 24, What is the mean of band d?

•  31

• 32

• 33

• 34

## Chapter 24: Measures of Central Tendency

Ex. 24.1Ex. 24.2Ex. 24.3Ex. 24.4Others

## RD Sharma solutions for Mathematics for Class 9 chapter 24 - Measures of Central Tendency

RD Sharma solutions for Mathematics for Class 9 chapter 24 (Measures of Central Tendency) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics for Class 9 chapter 24 Measures of Central Tendency are Introduction of Statistics, Collection of Data, Presentation of Data, Graphical Representation of Data, Measures of Central Tendency.

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