Sandeep Garg 2018 Solutions for Class 11 Commerce Economics Chapter 4 Graphic Presentation are provided here with simple step-by-step explanations. These solutions for Graphic Presentation are extremely popular among Class 11 Commerce students for Economics Graphic Presentation Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Sandeep Garg 2018 Book of Class 11 Commerce Economics Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Sandeep Garg 2018 Solutions. All Sandeep Garg 2018 Solutions for class Class 11 Commerce Economics are prepared by experts and are 100% accurate.

#### 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

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

#### 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

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

#### 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

 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

#### 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

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

#### 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

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

#### 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

Frequency polygon under discrete series can be represented as:

#### 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

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

#### 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

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

#### 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

 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

#### 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

Frequency Polygon (without histogram) under continuos series:

#### 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

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

#### 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

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.

#### 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.

(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

#### 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

#### 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

Time Series Graph

#### 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

#### 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.

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

#### 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

#### 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

 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

#### 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

Two-Variable Arithmetic Line Graph

#### 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

 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

#### 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.

 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

#### 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

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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