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Page No 7.39:

Question 1:

Draw a Line frequency graph of the following data:

Marks 10 20 30 40 50 60 70
Frequency 3 7 9 11 12 14 15

Answer:

The given data can be represented with the help of a line frequency graph as follows:

Page No 7.39:

Question 2:

Represent the following data by a histogram:

Marks in Statistics 0−10 10−20 40−60 60−80 80−100
No. of Students 12 28 60 48 30

Answer:

The given data can be represented with the help of a histogram.


Page No 7.39:

Question 3:

The following data relates to the marks in Economics of 70 students. Depict it through Histogram.

Marks 0−10 10−20 20−50 50−70 70−80
No. of Students 7 10 24 18 11

Answer:

Marks No. of student Adjusted/ Histogram
0 − 10
10 − 20
20 − 50
50 − 70
70 − 80
7
10
24
18
11
7
10
24 ÷ 3 = 8
18 ÷ 2 = 9
11

Page No 7.39:

Question 4:

Represent the following frequency distribution by a histogram.

Mid-Values 2.5 7.5 12.5 17.5 22.5
Frequency 5 10 30 15 6

Answer:

Here,

The difference between the two mid points is 5 therefore half of the difference, i.e. 2.5 will be added and subtracted from each mid-point to get the following class intervals.

 

Mid-Values Class Interval Frequency
2.5
7.5
12.5
17.5
22.5
0 − 5
5 − 10
10 − 15
15 − 20
20 − 25
5
10
30
15
6



Page No 7.39:

Question 5:

The frequency distribution of marks obtained by 60 students of a class in a college is given below:

Marks 30−34 35−39 40−44 45−49 50−54 55−59 60−64
No. of Students 3 5 12 18 14 6 2

Answer:

Converting the inclusive class intervals into exclusive class intervals, as given below:
 

Marks No. of students
29.5 − 34.5
34.5 − 39.5
39.5 − 44.5
44.5 − 49.5
49.5 − 54.5
54.5 − 59.5
59.5 − 64.5
3
5
12
18
14
6
2




Page No 7.39:

Question 6:

Draw a frequency polygon for the following data:

Items 4 5 6 7 8 9 10
Frequency 4 6 10 25 22 18 12

Answer:

Frequency polygon under discrete series can be represented as:

Page No 7.39:

Question 7:

Present the following data in the form of frequency polygon, using histogram.

Daily wages (₹) 60−80 80−100 100−120 120−140 140−160 160−180 180−200
No. of Workers 3 5 10 15 7 4 2

Answer:


For drawing a frequency polygon, we simply join the top mid points of the rectangles of the histogram using a straight line.



  



Page No 7.40:

Question 8:

The frequency distribution of marks obtained by students in a class test is given below:

Marks (mid-points) 45 55 65 75 85
No. of Students 5 9 12 8 2

Answer:

The given data can be represented with the help of a frequency polygon.


Page No 7.40:

Question 9:

You are given the following marks secured by 45 students in an examination:

Marks 20−29 30−39 40−49 50−59 60−69 70−79
No. of Students 4 10 12 9 7 3

Answer:

Marks No. of Students
19.5 − 29.5
29.5 − 39.5
39.5 − 49.5
49.5 − 59.5
59.5 − 69.5
69.5 − 79.5
4
10
12
9
7
3

Page No 7.40:

Question 10:

Depict the following frequency distribution with the help of frequency polygon

Mid-Values 5 15 25 35 45 55 65 75
Frequency 4 10 16 22 25 12 7 2

Answer:


Frequency Polygon (without histogram) under continuos series:

  

Page No 7.40:

Question 11:

Make a frequency curve of the following data:

Class-interval 20−40 40−60 60−80 80−100 100−120 120−140 140−160
Frequency 3 7 11 15 13 6 2

Answer:

Class Interval Frequency
20 − 40
40 − 60
60 − 80
80 − 100
100 − 120
120 − 140
140 − 160
3
7
11
15
13
6
2

Page No 7.40:

Question 12:

From the following information, construct, less than and more than ogive.

Daily wages (in ₹) 60−90 90−120 120−150 150−180 180−210
No. of Workers 11 14 25 12 8

Answer:

For constructing less than ogive, first the given frequency distribution must be converted into less than cumulative frequency distribution as follows.
 

Daily Wages No. of workers
Less than 90
Less than 120
Less than 150
Less than 180
Less than 210
11
25
50
62
70

We now plot the cumulative frequencies against the upper limit of class intervals. The curve obtained on joining the points so plotted is known as less than ogive.


For constructing more than ogive, first the given frequency distribution must be converted into more than cumulative frequency distribution as follows.
 
Daily Wages No. of workers
More than 60
More than 90
More than 120
More than 150
More than 180
70
70 − 11 = 59
59 − 14 = 45
45 − 25 = 20
20 − 12 = 8

We now plot the cumulative frequencies against the lower limit of class intervals. The curve obtained on joining the points so plotted is known as more than ogive.

Page No 7.40:

Question 13:

The table given below shows the amount of sales of 100 companies:

Sales (₹ in crores) 20−30 30−40 40−50 50−60 60−70 70−80
No. of Companies 7 12 15 30 22 14
With the help of information given above, prepare: (i) 'Less than' ogive; (ii) 'More than" ogive; and (iii) 'Less than' ogive.

Answer:

(i) For constructing less than ogive, first the given frequency distribution must be converted into less than cumulative frequency distribution as follows.
 

Sales No. of Companies
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80
7
19
34
64
86
100


We now plot the cumulative frequencies against the upper limit of class intervals. The curve obtained on joining the points so plotted is known as less than ogive.



(ii) For constructing more than ogive, first the given frequency distribution must be converted into more than cumulative frequency distribution as follows.
 
Sales No. of companies
More than 20
More than 30
More than 40
More than 50
More than 60
More than 70
100
100 − 7 = 93
93 − 12 = 81
81 − 15 = 66
66 − 30 = 36
36 − 22 = 14

We now plot the cumulative frequencies against the lower limit of class intervals. The curve obtained on joining the points so plotted is known as more than ogive.


   

(iii) 'Less than' and 'More than' ogive

 

Page No 7.40:

Question 14:

Represent the following data relating to annual profits of a company with the help of suitable graph.

Year 2008 2009 2010 2011 2012 2013 2014
Profits (in ₹ Crores) 25 37 45 35 50 54 60

Answer:


Page No 7.40:

Question 15:

The following data relates to rubbers imports of a company for seven years. Present the information using a time series graph:

Year 2009 2010 2011 2012 2013 2014 2015
Imports (₹ Crores) 125 175 150 125 200 150 175

Answer:

Time Series Graph



Page No 7.41:

Question 16:

Prepare a graph to represent following data of imports and exports of a commodity from 2008 to 2014.

Year 2008 2009 2010 2011 2012 2013 2014
Imports (₹ crores) 15 22 35 45 52 55 60
Exports (₹ crores) 20 28 42 60 65 70 75

Answer:


Page No 7.41:

Question 17:

The data relating to daily pocket money allowance of the students of class XI of a school is given below:

Pocket Money (₹) 0−5 5−10 10−15 15−20 20−25 25−30
No. of Students 7 12 18 25 10 3
Construct a histogram.

Answer:

Pocket Money No. of Students
0 − 5
5 − 10
10 − 15
15 − 20
20 − 25
25 − 30
7
12
18
25
10
3

Page No 7.41:

Question 18:

The following tale gives details of expenditure incurred by a company from 2009 to 2015:

Years 2009 2010 2011 2012 2013 2014 2015
Expenditure (₹ in Lakhs) 12 18 22 15 25 35 42

Answer:


Page No 7.41:

Question 19:

Make histogram and frequency polygon from the following distribution.

Class-interval 0−20 20−30 30−40 40−60 60−100
Frequency 10 4 6 14 16

Answer:

Class Interval Frequency Adjusted Frequency for Histogram
0 − 20
20 − 30
30 − 40
40 − 60
60 − 100
10
4
6
14
16
10 ÷ 2 = 5
4
6
14 ÷ 2 = 7
16 ÷ 4 = 4

Page No 7.41:

Question 20:

The following table gives data on the production and sales of factory for 5 years between 2011 to 2105. Make a two-Variable Arithmetic Line Graph.

Year 2011 2012 2013 2014 2015
Production (in tonnes) 20 24 30 42 55
Sales (₹ in crores) 28 32 40 57 65

Answer:

Two-Variable Arithmetic Line Graph


Page No 7.41:

Question 21:

Present the data given in the table below in the form of histogram.

Mid-point 15 25 35 45 55 65 75
Frequency 5 12 20 18 16 25 22

Answer:

Mid point Class interval Frequency
15
25
35
45
55
65
75
10 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
70 − 80
5
12
20
18
16
25
22

Page No 7.41:

Question 22:

In a certain colony,  40 households were selected. The data on monthly income (₹'000) is given below:

20 12 35 55 40 14 35 8 18 11
60 11 35 50 45 20 16 7 15 70
18 65 62 16 21 19 24 11 19 35
13 25 43 15 30 40 25 55 22 35
(i) Make a frequency distribution taking class interval of 10 marks. (Take first class interval as 0−10).
(ii) Draw a histogram and a frequency polygon form the frequency distribution.

Answer:

Class Interval Tally Frequency
0 − 10 2
10 − 20 14
20 − 30   7
30 − 40 6
40 − 50 4
50 − 60 3
60 −70 3
70 − 80 1
    40

Page No 7.41:

Question 23:

Draw a 'Less than' and 'More than' ogive from the following distribution:

Profits (₹ in Lakhs) 10−20 20−30 30−40 40−50 50−60 60−70
No. of Companies 4 7 10 20 17 2

Answer:

For constructing less than ogive, first the given frequency distribution must be converted into less than cumulative frequency distribution as follows.
 

Less than No. of Companies
Less than 20
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
4
4 + 7 = 11
11 + 10 = 21
21 + 20 = 41
41 + 17 = 58
58 + 2 = 60

We now plot the cumulative frequencies against the upper limit of class intervals. The curve obtained on joining the points so plotted is known as less than ogive.



For constructing more than ogive, first the given frequency distribution must be converted into more than cumulative frequency distribution as follows.
 
More than No. of companies
More than 10
More than 20
More than 30
More than 40
More than 50
More than 60
60
60 − 4 = 56
56 − 7 = 49
49 − 10 = 39
39 − 20 = 19
19 − 17 = 2

We now plot the cumulative frequencies against the lower limit of class intervals. The curve obtained on joining the points so plotted is known as more than ogive.



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