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

## Chapter 22: Tabular Representation of Statistical Data

Ex. 22.10Ex. 22.20Others

#### Chapter 22: Tabular Representation of Statistical Data Exercise 22.10 solutions [Pages 15 - 18]

Ex. 22.10 | Q 1 | Page 15

What do you understand by the word “statistics” in
(i) Singular form
(ii) Plural form?

Ex. 22.10 | Q 2 | Page 15

Describe some fundamental characteristics of statistics.

Ex. 22.10 | Q 3.1 | Page 15

What is primary data?

Ex. 22.10 | Q 3.2 | Page 15

What secondary data?

Ex. 22.10 | Q 3.3 | Page 15

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

Ex. 22.10 | Q 4 | Page 16

Why do we group data?

Ex. 22.10 | Q 5.1 | Page 16

Explain the meaning of the term Variable.

Ex. 22.10 | Q 5.2 | Page 16

Explain the meaning of the term Class-integral.

Ex. 22.10 | Q 5.3 | Page 16

Explain the meaning of the term Class-size.

Ex. 22.10 | Q 5.4 | Page 16

Explain the meaning of the term Class-mark.

Ex. 22.10 | Q 5.5 | Page 16

Explain the meaning of the term Frequency.

Ex. 22.10 | Q 5.6 | Page 16

Explain the meaning of the term Class limits.

Ex. 22.10 | Q 5.7 | Page 16

Explain the meaning of the term True class limits.

Ex. 22.10 | Q 6 | Page 16

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?

Ex. 22.10 | Q 7 | Page 16

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.

Ex. 22.10 | Q 8 | Page 16

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

Ex. 22.10 | Q 9 | Page 16

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.
(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?

Ex. 22.10 | Q 10 | Page 16

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?

Ex. 22.10 | Q 11 | Page 17

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?

Ex. 22.10 | Q 12 | Page 17

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.

Ex. 22.10 | Q 13 | Page 17

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

Ex. 22.10 | Q 14 | Page 17

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.

Ex. 22.10 | Q 15 | Page 17

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.

Ex. 22.10 | Q 16 | Page 17

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.

Ex. 22.10 | Q 17 | Page 17

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.

Ex. 22.10 | Q 18 | Page 17

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.

Ex. 22.10 | Q 19 | Page 17

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.

Ex. 22.10 | Q 20 | Page 18

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.

Ex. 22.10 | Q 21 | Page 18

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

Ex. 22.10 | Q 22 | Page 18

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?

Ex. 22.10 | Q 23 | Page 18

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.

#### Chapter 22: Tabular Representation of Statistical Data Exercise 22.20 solutions [Pages 24 - 25]

Ex. 22.20 | Q 1 | Page 24

Define cumulative frequency distribution.

Ex. 22.20 | Q 2 | Page 24

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

Ex. 22.20 | Q 3 | Page 24

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:

Ex. 22.20 | Q 4 | Page 24

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

 Age (inyears): 10-20 20-30 30-40 40-50 50-60 60-70 No. ofPatients: 90 50 60 80 50 30

Construct a cumulative frequency distribution.

Ex. 22.20 | Q 5 | Page 24

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.

Ex. 22.20 | Q 6 | Page 24

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.

Ex. 22.20 | Q 7 | Page 24

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
Ex. 22.20 | Q 8 | Page 25

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.

Ex. 22.20 | Q 9 | Page 25

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

#### Chapter 22: Tabular Representation of Statistical Data solutions [Pages 26 - 27]

Q 1 | Page 26

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

•  class intervals

• range

• frequency

• upper limits

Q 2 | Page 26

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

• frequency

• mean

• range

•  class-intervals

Q 3 | Page 26

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

•  mid-points

•  class size

• frequency

• mean

Q 4 | Page 26

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

Q 5 | Page 26

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

Q 6 | Page 26

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

Q 7 | Page 27

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

•  variation

• frequency

• cumulative frequency

• class-size

Q 8 | Page 27

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

Q 9 | Page 27

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

Q 10 | Page 27

Tallys are usually marked in a bunch of

• 3

• 4

• 5

• 6

Q 11 | Page 27

Let 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 − 2l

## Chapter 22: Tabular Representation of Statistical Data

Ex. 22.10Ex. 22.20Others

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

RD Sharma solutions for Class 9 Maths chapter 22 (Tabular Representation of Statistical Data) 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 by R D Sharma (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

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

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