Selina Concise Class 10 Math Chapter 23 Graphical Representation (Histograms and ogives) Solutions

Selina Concise Class 10 Math Chapter 23 Graphical Representation (Histograms and ogives) Solutions

 

Graphical Representation

(Histograms and ogives)

 

(Q1) Draw histograms for the following frequency distributions

(i)

Class interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
Frequency 12 20 26 18 10 6

 

Solution:

First we have to draw given table

Class Interval Frequency
0 – 10 12
10 – 20 20
20 – 30 26
30 – 40 18
40 – 50 10
50 – 60 6

 

(9) Graphical Representation

 

(i)

How to draw histogram

(1) First we have write scale

(2) Draw x-axis and y-axis

(3) Write frequency on y-axis and class interval on x-axis

(4) Draw rectangle type histograms on x-axis and corresponding frequencies as heights of histogram.

(ii)

Class Interval 10 – 16 16 – 22 22 – 28 28- 34 34 – 40
Frequency 15 23 30 20 16

 

Solution:

First we have draw given table

Class Interval

Frequency

10 – 16 15
16 – 22 23
22 – 28 30
28 – 34 20
34 – 40 16

 

* How to construct histograms?

(1) First we have draw x-axis and y-axis 

(2) On x-axis we have to write class interval

(3) On y-axis we have to frequency

(4) This frequency is the height of histogram

(5) Histogram is like a rectangular shape

 

 

(iii)

 

Class interval 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79
Frequency 24 16 09 15 20

 

Solution:

We can see that the given table, class interval is not continue so, first we have to do continue class interval.

Class interval (Given) Class interval (New) Frequency
30 – 39 29.5 –   39.5 24
40 –  49 39.5 – 49.5 16
50 – 59 49.5 – 59.5 09
60 – 69 59.5 – 69.5 15
70 – 79 69.5 – 79.5 20

 

In lower class we have to subtract 0.5 [30 – 0.5 = 29.5] and in upper class we have to add 0.5 [39+0.5 = 39.5] 

 

(iii)

How to construct histograms

(1) First we have to do continue class interval

(2) Draw x-axis and y-axis

(3) On – x-axis we have to write class interval

(4) On y-axis we have to write frequency and frequency is a height of histogram.

 

(iv)

 

Class Marks 16 24 32 40 48 56 64
Frequency 8 12 15 18 25 19 10

 

Solution:

First we have to do class interval column.

In classes marks,

First class mark is 16 and second is 24 so the difference is 8 (24 – 16 = 8)

So the class interval is 12 – 20

(20 – 12 = 8)

 

Class Marks

Class interval

Frequency

16 12 – 20 8
24 20 – 28 12
32 28 – 36 15
40 36 – 44 18
48 44 – 52 25
56 52 – 60                                      19
64 60 – 68 10

 

(iv) How to construct histogram?

(1) First we have to draw x-axis and y-axis

(2) Convert class mark into class interval

(3) On x-axis we have to write class interval and y-axis we have to write frequency

(4) Frequency is a height of histogram

 

(Q2)

Draw cumulative frequency curve (ogive) for each of the following distributions.

(i)

Class interval                10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40
Frequency 10 15 17 12 10 08

 

Solution:

Class interval Frequency
10 – 15 10
15 – 20 15
20 – 25 17
25 – 30 12
30 – 35 10
35 – 40 08

 

* How to draw cumulative frequency curve or construction?

(1) First we have to draw x-axis and y-axis

(2) On x-axis we have to write class interval and on y-axis we have to write frequency

(3) Join the mid points of the rectangular or histogram to obtain the cumulative frequency curve

 

 

(ii) 

Class interval 10 -19 20 – 29 30 – 39 40 – 49 50 – 59
Frequency 23 16 15 20 12

 

Solution:

First we have to do continue class interval because given class interval is not continue and after we have to draw cumulative frequency column.

Class Interval (Given) Class interval (New) Frequency Cumulative frequency
10 – 19 9.5 – 19.5 23 23
20 – 29 19.5 – 29.5 16 23+16 = 39
30 – 39 29.5 – 39.5 15 39+15 = 54
40 – 49 39.5 – 49.5 20 54+20 = 74
50 – 59 49.5 – 59.5 12 74+12 = 86
Total 86

 

(Q2) (ii)

How to draw graph?

(1) First we have to draw x-axis and y-axis

(2) Convert class interval into continue class interval [In lower class 10-0.5 = 9.5] Subtract 0.5 from lower class.

(3) And draw cumulative frequency column

(4) On x-axis we have to write class interval and on y-axis we have to write frequency.

 

(Q3)

Draw an ogive each of the following distributions

(i)

Marks obtained Less than 10 Less than 20 Less than 30 Less than 40 Less than 50
Number of students 8 25 38 50 67

 

Solution:

First we have draw a given table:

Marks Obtain Number of students
Less than10 8
Less than 20 25
Less than 30 38
Less than 40 50
Less than 50 67

 

* How to draw or construct ogive?

(1) First we have to draw x-axis and y-axis

(2) On X-axis we have to write marks obtained and on y-axis we have to write number of students

(3) After we have to plot points (10, 8), (20, 25), (30, 38) (40, 50) and (50, 57) on the graph paper.

(4) After join this points for free hand (Not use rular)

 

ii)

Age in years (less than) 10 20 30 40 50 60 70
Cumulative frequency 0 17 32 37 53 58 65

 

Solution:

First we have to draw table

Age in years (Less than) Cumulative frequency
10 0
20 17
30 32
40 37
50 53
60 58
70 65

 

* How to draw or construct ogiven?

(1) First we have draw x-axis and y-axis

(2) On x-axis we have write age in years and on y-axis we have write cumulative frequency.

(3) After we have to plot points (10,0), (20,17), (37,32) (40,37), (50,53), (60,58), an (70,65)

(4) After join this ploted point for free hand (Not use rular)

 

(Q4) Construct a frequency table for the number given below using the class intervals 21-30, 31-40, etc,

75, 67, 57, 50, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36, 47

Use the table obtained to draw:

Solution:

Firs we have to draw table –

Class interval Tally Frequency Cumulative Frequency
21 – 30 II II 4 4

31 – 40

IIII

9 9+4 = 13
41 – 50 IIII 9 13+9 = 22
51 – 60 III 7 22+7 = 29
61 – 70 II 8 29+8 = 37
71 – 80 III 3 37+3 = 40

 

Tally: In 21-30 there are 4 numbers so, we have to draw four lines.

In 31 – 40 there are 9 numbers so, we have to draw 9 lines in tally table

In 41 – 50 there are 9 numbers so, we have to draw 9 lines

In 51 – 60 there are 7 numbers so, we have to draw 7 lines

In 61 – 70 there are 8 numbers so, we have to draw 8 lines

In 71 – 80 there are 3 numbers so, we have to draw 3 lines.

 

 

 

Here is your solution of Selina Concise Class 10 Math Chapter 23 Graphical Representation (Histograms and ogives)

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