#### 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

## Chapter 22: Tabular Representation of Statistical Data

#### 22.1 [Pages 15 - 18]

### RD Sharma solutions for Mathematics for Class 9 Chapter 22 Tabular Representation of Statistical Data 22.1 [Pages 15 - 18]

What do you understand by the word “statistics” in

(i) Singular form

(ii) Plural form?

Describe some fundamental characteristics of statistics.

What is primary data?

What secondary data?

Which of the two – the primary or the secondary data – is more reliable and why?

Why do we group data?

Explain the meaning of the term Variable.

Explain the meaning of the term Class-integral.

Explain the meaning of the term Class-size.

Explain the meaning of the term Class-mark.

Explain the meaning of the term Frequency.

Explain the meaning of the term Class limits.

Explain the meaning of the term True class limits.

The ages of ten students of a group are given below. The ages have been recorded in years

and months:

8 – 6, 9 – 0, 8 – 4, 9 – 3, 7 – 8, 8 – 11,8 – 7, 9 – 2, 7 – 10, 8 – 8

(i) What is the lowest age?

(ii) What is the highest age?

(iii) Determine the range?

The monthly pocket money of six friends is given below: Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs.

25, Rs. 45.

(i) What is the highest pocket money?

(ii) What is the lowest pocket money?

(iii) What is the range?

(iv) Arrange the amounts of pocket money in ascending order.

Write the class-size in each of the following:

(i) 0 – 4, 5 – 9, 10 – 14

(ii) 10 – 19, 20 – 29, 30 – 39

(iii) 100 – 120, 120 – 140, 160 – 180

(iv) 0 – 0.25, 0.25 – 0.50, 0.50 – 0.75

(v) 5 – 5.01, 5.01 − 5.02, 5.02 – 5.03

The final marks in mathematics of 30 students are as follows:

53, 61, 48, 60, 78, 68, 55, 100,67,90

75,88,77,37,84,58,60,48,62,56

44, 58, 52, 64, 98, 59, 70, 39, 50, 60

(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second group etc.

Now answer the following:

(ii) What is the highest score?

(iii) What is the lowest score?

(iv) What is the range?

(v) If 40 is the pass mark how many have failed?

(vi) How many have scored 75 or more?

(vii) Which observations between 50 and 60 have not actually appeared?

(viii) How many have scored less than 50?

The weights of new born babies (in kg) in a hospital on a particular day are as follows:

2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4

(i) Rearrange the weights in descending order.

(ii) Determine the highest weight.

(iii) Determine the lowest weight.

(iv) Determine the range.

(v) How many babies were born on that day?

(vi) How many babies weigh below 2.5 kg?

(vii) How many babies weigh more than 2.8 kg?

(viii) How many babies weigh 2.8 kg?

The number of runs scored by a cricket. player in 25 innings are as follows:

26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 1.5, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64,47.

(i) Rearrange these runs in ascending order.

(ii) Determine the player, is highest score.

(iii) How many times did the player not score a run?

(iv) How many centuries did he score?

(v) How many times did he score more than 50 runs?

The class size of a distribution is 25 and the first class-interval is 200-224. There are seven

class-intervals.

(i) Write the class-intervals.

(ii) Write the class-marks of each interval.

Write the class size and class limits in each of the following:

(i) 104, 114, 124, 134, 144, 154, and 164

(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102

(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

Following data gives the number of children in 40 families:

1,2,6,5,1,5, 1,3,2,6,2,3,4,2,0,0,4,4,3,2,2,0,0,1,2,2,4,3, 2,1,0,5,1,2,4,3,4,1,6,2,2.

Represent it in the form of a frequency distribution.

The marks scored by 40 students of class IX in mathematics are given below:

81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70,

83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.

Prepare a frequency distribution with class size of 10 marks.

The heights (in cm) of 30 students of class IX are given below:

155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153

Prepare a frequency distribution table with 160-164 as one of the class intervals.

The monthly wages of 30 workers in a factory are given below:

83.0, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808,

812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.

Represent the data in the form of a frequency distribution with class size 10.

The daily maximum temperatures (in degree celsius) recorded in a certain city during the

month of November are as follows:

25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5,

20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1

Represent them as a frequency distribution table with class size 1°C.

Construct a frequency table with equal class intervals from the following data on the monthly

wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as

210-230 (230 not included):

220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292,

254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

The blood groups of 30 students of class VIII are recorded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B,O

Represent this data in the form of a frequency distribution table. Find out which is the most Common and which is the rarest blood group among these students.

Three coins were tossed 30 times. Each time the number of head occurring was noted down

as follows:

0 1 2 2 1 2 3 1 3 0

1 3 1 1 2 2 0 1 2 1

3 0 0 1 1 2 3 2 2 0

Thirty children were asked about the number of hours they watched T.V. programmers in the previous week. The results were found as follows:

1 | 6 | 2 | 3 | 5 | 12 | 5 | 8 | 4 | 8 |

10 | 3 | 4 | 12 | 2 | 8 | 15 | 1 | 17 | 6 |

3 | 2 | 8 | 5 | 9 | 6 | 8 | 7 | 14 | 12 |

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 – 10.

(ii)How many children watched television for 15 or more hours a week?

The daily minimum temperatures in degrees Ce1siu& recorded in a certain Arctic region are

as follows:

−12.5, −10.8, −18.6, −8.4, −10.8, −4.2, −4.8, −6.7, −13.2, −11.8, −2.3, 1.2, 2.6, 0, 2.4,

0, 3.2, 2.7, 3.4, 0, − 2.4, − 2.4, 0, 3.2, 2.7, 3.4, 0, − 2.4, − 5.8, -8.9, 14.6, 12.3, 11.5, 7.8,2.9.

Represent them as frequency distribution table taking − 19.9 to − 15 as the first class

interval.

#### 22.2 [Pages 24 - 25]

### RD Sharma solutions for Mathematics for Class 9 Chapter 22 Tabular Representation of Statistical Data 22.2 [Pages 24 - 25]

Define cumulative frequency distribution.

Explain the difference between a frequency distribution and a cumulative frequency distribution.

The marks scored by 55 students in a test are given below:

Marks | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |

No. of students | 2 | 6 | 13 | 17 | 11 | 4 | 2 |

Prepare a cumulative frequency table:

Following are the ages of360 patients getting medical treatment in a hospital on a day:

Age (in years): |
10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

No. of Patients: |
90 | 50 | 60 | 80 | 50 | 30 |

Construct a cumulative frequency distribution.

The water bills (in rupees) of 32 houses in a certain street for the period 1.1.98 to. 31.3.98 are given below:

56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59.

Tabulate the data and resent the data as a cumulative frequency table using 70-79 as one of the class intervals.

The number of books in different shelves of a library are as follows:

30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20

19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34,

38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25

28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23,

43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.

Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

Weight (in kg) | No. of students |

Below 25 | 0 |

Below 30 | 24 |

Below 35 | 78 |

Below 40 | 183 |

Below 45 | 294 |

Below 50 | 408 |

Below 55 | 543 |

Below 60 | 621 |

Below 65 | 674 |

Below 70 | 685 |

The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:

Consumption (in kW) | No. of Factories |

Below 240 | 1 |

Below 270 | 4 |

Below 300 | 8 |

Below 330 | 24 |

Below 360 | 33 |

Below 390 | 38 |

Below 420 | 40 |

(i) Represent this as a frequency distribution table.

(ii) Prepare a cumulative frequency table.

Given below is a cumulative frequency distribution table showing the ages of people living in a locality:

Ace in years | No. of persons |

Above 108 | 0 |

Above 96 | 1 |

Above 84 | 3 |

Above 72 | 5 |

Above 60 | 20 |

Above 48 | 158 |

Above 36 | 427 |

Above 24 | 809 |

Above 12 | 1026 |

Above 0 | 1124 |

Prepare a frequency distribution table

#### [Pages 26 - 27]

### RD Sharma solutions for Mathematics for Class 9 Chapter 22 Tabular Representation of Statistical Data [Pages 26 - 27]

Mark the correct alternative in each of the following: Tally marks are used to find

class intervals

range

frequency

upper limits

The difference between the highest and lowest values of the observations is called

frequency

mean

range

class-intervals

The difference between the upper and the lower class limits is called

mid-points

class size

frequency

mean

In the class intervals 10-20, 20-30, 20 is taken in

the interval 10-20

the interval 20-30

both intervals 10-20, 20-30

none of the intervals

In a frequency distribution, the mid-value of a class is 15 and the class intervals is 4. The lower limit of the class is

10

12

13

14

The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:

47 and 37

37 and 47

37.5 and 47.5

47.5 and 37.5

The number of times a particular item occurs in a given data is called its

variation

frequency

cumulative frequency

class-size

The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is

35.6

33.1

30.6

28.1

The following marks were obtained by the students in a test:

81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62

The range of the marks is

9

17

27

33

Tallys are usually marked in a bunch of

3

4

5

6

Let *l *be the lower class limit of a class-interval in a frequency distribution and *m* be the mid point of the class. Then, the upper class limit of the class is

*m*+ \[\frac{l + m}{2}\]*l*+ \[\frac{m + l}{2}\]2m − 1

m − 2

*l*

## Chapter 22: Tabular Representation of Statistical Data

## RD Sharma solutions for Mathematics for Class 9 chapter 22 - Tabular Representation of Statistical Data

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Concepts covered in Mathematics for Class 9 chapter 22 Tabular Representation of Statistical Data are Introduction of Statistics, Collection of Data, Presentation of Data, Graphical Representation of Data, Measures of Central Tendency.

Using RD Sharma Class 9 solutions Tabular Representation of Statistical Data exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

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