RD SHARMA Solutions for Class 9 Maths Chapter 23 - Graphical Representation of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data Exercise 23.42

Question 1

Which one of the following is not the graphical representation of statistical data?

(a) Bar grpah

(b) Histogram

(c) Frequency polygon

(d) Cumulative frequency distribution

Solution 1

Bar graphs, Histogram, Frequency polygon are methods of graphical representation of statistical data.

A Bar graph is a pictorial representation of the numerical Data. while Histogram is a graphical representation

of a Frequency distribution in the form of rectangles.

A Frequency polygon of a given Frequency distribution is another method of representing frequency distribution graphically.

But a cumulative frequency distribution is a table in which cumulative frequencies are distributed over various classes.

Thus, Cumulative frequency distribution is not a method of graphical representation.

Hence, correct option is (d).

Question 2

In a frequency distribution, ogives are graphical representation of

(a) Frequency

(b) Relative frequency

(c) Cumulative frequency

(d) Raw data

Solution 2

A curve that Represents the cumulative Frequency distribution of grouped data is called an ogive or cumulative frequency curve.

Hence, correct option is (c)

Question 3

A frequency polygon is constructed by plotting frequency of the class interval and the

(a) upper limit of the class

(b) lower limit of the class

(c) mid value of the class

(d) any values of the class

Solution 3

A Frequency Polygon is drawn by joining the mid-points of first and last class intervals to the mid-points of the imagined classes adjacent to them.

Hence, correct option is (c). 

Chapter 23 - Graphical Representation of Statistical Data Exercise 23.43

Question 1

In a histogram the area of each rectangle is proportional to

(a) the class mark of the corresponding class interval

(b) the class size of the corresponding class interval

(c) frequency of the corresponding class interval

(d) cumulative frequency of the corresponding class interval

Solution 1

In a Histogram, the area of each rectangle is proportional to the Frequency of the corresponding class-interval.

Hence, correct option is (c).

Question 2

In the 'less than' type of ogive the cumulative frequency is plotted against

(a) the lower limit of the concerned class interval

(b) the upper limit of the concerned class interval

(c) the mid-value of the concerned class interval

(d) any value of the concerned class interval

Solution 2

In a less than type ogive, the cumulative frequency is plotted against the upper limit of the concerned class interval.

Hence, correct option is (b).

Question 3

In a histogram, the class intervals or the groups are taken along

(a) Y-axis

(b) X-axis

(c) both of X-axis and Y-axis

(d) in between X and Y axis

Solution 3

In a Histogram, the class-intervals are represented or taken along X-axis, and frequency on Y-axis.

Hence, correct option is (b).

Question 4

A histogram is a pictorial representation of the grouped data in which class intervals and frequency are respectively taken along

(a) vertical axis and horizontal axis

(b) vertical axis only

(c) horizontal axis only

(d) horizontal axis and vertical axis

Solution 4

In a Histogram, the class-intervals are represented or taken along Horizontal axis (X-axis) and frequency on Vertical axis (Y-axis).

Hence, correct option is (d).

Question 5

In a histogram, each class rectangle is constructed with base as

(a) frequency

(b) class-intervals

(c) range

(d) size of the class

Solution 5

In a Histogram, each class rectangle is constructed with base as (a - b) i.e. a class intervals from a to b ..... b to c etc.

Hence, correct option is (b).

Chapter 23 - Graphical Representation of Statistical Data Exercise Ex. 23.1

Question 1
The following table shows the daily production of T.V. sets in an industry for 7 days a week:

Day Mon Tue Wed Thurs Fri Sat Sun
No. of T.V. sets 300 400 150 250 100 350 200


Represent the above information by a pictograph.
Solution 1
The given information can be represented through a pictograph as follows:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 2
The following table shows the number of Maruti cars sold by five dealers in a particular month:

Dealer Saya Bagga Links D.D. Motors Bhasin Motors Competent
Cars sold 60 40 20 15 10


Represent the above information by a pictograph.
Solution 2
The given information can be represent through a pictograph as follows:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 3
The population of Delhi State in different census years is as given below:

Census Year 1961 1971 1981 1991 2001
Population In Lakhs 30 55 70 110 150


Represent the above information with the help of bar graph.
Solution 3
To represent the data by a bar graph, draw horizontal and vertical axes. Mark census year on the horizontal axis and the population on the vertical axis.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 4
Read the bar graph shown in figure and answer the following questions:

(i) What is the information given by the bar graph?

(ii) How many tickets of Assam state lottery were sold by the agent?

(iii) Of which state, were the maximum number of tickets sold?

(iv) State whether true or false.

      The maximum number of tickets sold is three the minimum number of tickets sold.

(v) Of which state were the minimum number of tickets sold?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 4
(i) The given bar graph represents the number of tickets of different state lotteries sold by an agent on a day.

(ii) The number of tickets of Assam state lottery sold by the agent is 40.

(iii) Haryana

(iv) The minimum number of tickets sold = 20

      The maximum number of tickets sold = 100

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

So, the given statement is false.

(v) Rajasthan
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical DataRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 9

Read the following bar graph and answer the following questions:

(i) What information is given by the bar graph?

(ii) Which state is the largest producer of rice?

(iii) Which state is the largest producer of wheat?

(iv) Which state has total production of rice and wheat as its maximum?

(v) Which state has total production of wheat and rice minimum?

 


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Solution 9

(i) It gives information regarding rice and wheat production in various states of India.

(ii) W.B is the largest produer of rice.

(iii) U.P is the largest producer of wheat.

(iv) The total production of rice and wheat is maximum in U.P.

(v) The total production of rice and wheat is minimum in Maharashtra.

Question 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 12
Read the bar graph given in fig., and answer the following questions:

(i) What information is given by the bar graph?

(ii) What was the crop-production of rice in 1970-71?

(iii) What is the difference between the maximum and minimum production of rice?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 12
(i) It gives information regarding the production of rice crop in India in different years.

(ii) The crop-production of rice in 1970-71 = 42.5 lakh tonnes.

(iii) The difference between the maximum and minimum production of rice = 55 - 22 = 33 lakh tonnes.
Question 13
Read the bar graph given fig., and answer the following questions:

(i) What information does it give?

(ii) In which part the expenditure on education is maximum in 1980?

(iii) In Which part the expenditure has gone up from 1980 to 1990?

(iv) In which part the gap between 1980 and 1990 is maximum?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 13
(i) It gives the information about the public expenditure on education by various state subcontinents.

(ii) In Africa the expenditure on edcation is maximum in 1980.

(iii) In East Africa the expenditure has gone by from 1980 to 1990.

(iv) In Africa the gap between 1980 and 1990 is maximum.
Question 14
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 14
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 15
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 15
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 16
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 16
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 17
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 17
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data Exercise Ex. 23.2

Question 1
Explain the reading and interpretation of bar graphs.
Solution 1
The first step in reading a bar graph is to know what it represents or what is the information given by it. For this, we read the captions which are generally written just below the horizontal line (x-axis) and adjacent to vertical line (y-axis). After knowing that what does a bar graph represent, we read the scale so that we can know the precise values in the given data.

After reading a bar graph one must be able to draw certain condusions from it. Drawing some condusions from a given bar graph means interpretation of the bar graph.
Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 3
The following bar graph shows the results of an annual examination in a secondary school.

Read the bar graph (fig.,) and choose the correct alternative in each of the following

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

(i) The pair of classes in which the results of boys and girls are inversely proportional are:

(a) VI, VIII

(b) VI, IX

(c) VIII, IX

(d) VIII, X

(ii) The class having the lowest failure rate of girls is

(a) VII

(b) X

(c) IX

(d) VIII

(iii) The class having the lowest pass rate of students is

(a) VI

(b) VII

(c) VIII

(d) IX
Solution 3
(i) (b) VI, IX

(ii) (a) VII

(iii) (b) VII
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 7
The following data gives the amount of loans (in croroes of rupees) disbursed by a bank during some years:

Year 1992 1993 1994 1995 1996
Loan (in crores of rupees) 28 33 55 55 80


(i) Represent the above data with the help of a bar graph.

(ii) With the help of the bar graph, indicate the year in which amount of loan is not increased over that of the preceding year.
Solution 7

(i) Bar graph for the given data is as follows:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

(ii) In 1995, the amount of loan is not increased over that of the preceeding year.

Question 8
The following table shows the interest paid by a company (in lakhs):

Year 1995-96 1996-97 1997-98 1998-99 1999-2000
Interest (in lakhs of rupees) 20 25 15 18 30


Draw the bar graph to represent the above information.
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 9
The following data shows the average age of men in various countries in a certain year:

Country India Nepal China Pakistan U.K. U.S.A.
Average age (in years) 55 52 60 50 70 75


Represent the above information by a bar graph.
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 10
The following data gives the production of foodgrains (in thousand tonnes) for some years:

Year 1995 1996 1997 1998 1999 2000
Production (in thousand tonnes) 120 150 140 180 170 190


Represent the above data with the help of a bar graph.
Solution 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 11
(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

(ii) It is seen that the height of bar corresponding to year 1994 is the highest. Hence, the amount of manure manufactured by the company was maximum in 1994.

(iii) It is seen that the manure production decreased in the year 1995 and 1997.
Question 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 12
The bar graph of the given bata:
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

The course where estimated requirement is least is DCE
Question 13
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 13
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 14
The investment (in ten crores of rupees) of Life Insurance Corporation of India in different sectors are given below:

Sectors Investment (in ten crores of rupees)
Central Government Securities

State Government Securities

Securities guaranteed by the Government

Private Sectros

Socially oriented sectors (Plan)

Socially oriented sectors (Non-Plan)
45

11

23

18

46

11


Represent the above data with the help of a bar graph.
Solution 14
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 15
The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:

Years 1982-83 1983-84 1984-85 1985-86 1986-87
Value of Exports of Cotton Textiles (in crores of rupees) 300 325 475 450 550


Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding years.
Solution 15
The bar graph of the given data:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

In 1986-87 the rate of increases in exports is maximum over the precending year.
Question 16
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 16
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

It is seen from the graph that the quantity of goods carried in the years 1950-51 and 1965-66 are 20 crores tones and 9 crores tones. Clearly 20 is more than twice of 9. Hence, the statement is true.
Question 17
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 17
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 18
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 18
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data Exercise Ex. 23.3

Question 1
Construct a histogram for the following data:

Monthly School fee (in Rs.) 30-60 60-90 90-120 120-150 150-180 180-210 210-240
No. of Schools 5 12 14 18 10 9 4
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Question 7
The monthly profits (in Rs.) of 100 shops are distributed as follows:

Profits per shop: 0-50 50-100 100-150 150-200 200-250 250-300
No. of shops: 12 18 27 20 17 6


Draw a histogram for the data and show the frequency polygon for it.
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Graphical Representation Of Statistical Data

Chapter - Exercise

Solution 1
Solution 2