#### Chapters

Chapter 2: Exponents of Real Numbers

Chapter 3: Rationalisation

Chapter 4: Algebraic Identities

Chapter 5: Factorisation of Algebraic Expressions

Chapter 6: Factorisation of Polynomials

Chapter 7: Linear Equations in Two Variables

Chapter 8: Co-ordinate Geometry

Chapter 9: Introduction to Euclid’s Geometry

Chapter 10: Lines and Angles

Chapter 11: Triangle and its Angles

Chapter 12: Congruent Triangles

Chapter 13: Quadrilaterals

Chapter 14: Areas of Parallelograms and Triangles

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Heron’s Formula

Chapter 18: Surface Areas and Volume of a Cuboid and Cube

Chapter 19: Surface Areas and Volume of a Circular Cylinder

Chapter 20: Surface Areas and Volume of A Right Circular Cone

Chapter 21: Surface Areas and Volume of a Sphere

Chapter 22: Tabular Representation of Statistical Data

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Measures of Central Tendency

Chapter 25: Probability

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

## Chapter 24: Measures of Central Tendency

#### Chapter 24: Measures of Central Tendency Exercise 24.1 solutions [Pages 9 - 10]

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

find the mean height.

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

Find the mean of first five natural numbers .

Find the mean of all factors of 10.

Find the mean of first 10 even natural numbers.

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

Find the mean of first five multiples of 3.

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.

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.

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.

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.

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.

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.

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

excluded number.

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.

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

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

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.

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.

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`(x_{i} - x ) = 0

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

(i) `sum _(i = 1)^n`(x_{i} - 12) = - 10 `sum _(i = 1)^n`(x_{i} - 3) = 62

(ii) `sum _(i = 1)^n` (x_{i} - 10) = 30 `sum _(i = 6)^n` (x_{i} - 6) = 150 .

The sums of the deviations of a set of n values 𝑥_{1}, 𝑥_{2}, … . 𝑥_{11} measured from 15 and −3 are − 90 and 54 respectively. Find the valùe of n and mean.

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

If x is the mean of the ten natural numbers `x_1, x_2 , x_3+....... + x_10` show that (x_{1} -x) + (x_{2} - x) +.........+ (x_{10} - x)` = 0

#### Chapter 24: Measures of Central Tendency Exercise 24.2 solutions [Pages 14 - 16]

Calculate the mean for the following distribution:

x : | 5 | 6 | 7 | 8 | 9 |

f : | 4 | 8 | 14 | 11 | 3 |

Find the mean of the following data:

x : | 19 | 21 | 23 | 25 | 27 | 29 | 31 |

f : | 13 | 15 | 16 | 18 | 16 | 15 | 13 |

Find the mean of the following distribution:

x : | 10 | 12 | 20 | 25 | 35 |

F : | 3 | 10 | 15 | 7 | 5 |

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 |

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 |

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

x: | 5 | 10 | 15 | 20 | 25 |

f : | 6 | p | 6 | 10 | 5 |

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 |

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 |

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 |

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 |

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.

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 | f_{1} |
32 | f_{2} |
19 | Total =120 |

#### Chapter 24: Measures of Central Tendency Exercise 24.3 solutions [Page 18]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

median is 25, find x.

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?

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.

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.

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

#### Chapter 24: Measures of Central Tendency Exercise 24.4 solutions [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.

Find the mode from the following data:

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

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

Find the mode of the following data :

14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18

Find the mode of the following data :

7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7

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.

#### Chapter 24: Measures of Central Tendency solutions [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.

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

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 \[\frac{x}{6}\] .

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

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

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

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.

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

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

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

#### Chapter 24: Measures of Central Tendency solutions [Pages 21 - 22]

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

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

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`

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

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

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

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

10

12

14

16

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

Mode is

least frequent value

middle most value

most frequent value

none of these

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

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

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

0

*n*− 1*n**n*+ 1

*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.

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

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*?

31

32

33

34

## Chapter 24: Measures of Central Tendency

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

#### Textbook solutions for Class 9

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

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

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