**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Bar-Diagram**

Contents

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Bar chart or graph is one of the oldest and most commonly used graph for presenting data. It is a chart with rectangular bars (equidistant from each other) with lengths proportional to the values they represent. The width of the bars is shown merely for attention.

In this method of data representation, the data is plotted on the x and y axis as bars.

One of the axis (normally the x-axis) of the bar diagram represents a discrete variable while the other axis represents the scale for one or more continuous variable. Each bar diagram has title indicating the subject matter represented in the diagram.

**Types of Graph/Chart**

**1. Simple Bar Diagram** A simple bar diagram relates to only one variable.

**2. Sub-divided Bar** **Diagram** A sub-divided bar diagram is used to represent various parts of total magnitude of a given variable.

**3. Multiple Bar Diagram** In this type, two or more bars are constructed adjoining each bar either to represent either , different components of a total or to show multiple variables.

**Directions (Examples 1 -5) Study the graph and answer the questions given below. ssc (10+2)2011**

**1. What is the difference in profit between 1983 and 1984 (in lakh of Rs)?**

(a) No profit

(b) 5

(c) 10

(d) 15

**2. The number of years in which the income is more than the average income of the given years is**

(a) one

(b) two

(c) three

(d) four

**3. The ratio of the average income of all the years to the average profit is**

(a) 24 :13

(b) 48 :17

(c) 12 : 7

(d) 6 : 5

**4.Percentage increase in profit in 1986 over 1982 is**

(a) 150%

(b) 120%

(c) 100%

(d) 80%

**5. The total income exceeds the total expenditure over the years 1982 to 1986 by**

(a) Rs 85 lakh

(b) Rs 105 lakh

(c) Rs 115 lakh

(d) Rs 120 lakh

**Illustration for Bar Diagram**

The diagram above shows the survey of 6 yr for the sales of mobile phones.

Here, x-axis shows the years which were considered for survey and y-axis shows the quantity of sales.

**(a) Histogram**

To understand histogram, we need to know the word frequency.

**Frequency** It is the number of occurrences of a repeating event per unit.

**Histogram** It is a representation of tabulated frequencies. This representation is done with the help of adjacent rectangles erected over discrete intervals.

**Different Components of Histogram**

**Height of the Rectangular Bars** It shows frequency density of the interval, i.e., the frequency divided by the

width of the interval.

**Area Covered by the Bars** This area shows the frequency of the observations in the interval.

**Total Area of Histogram** This area is equal to the number of data.

**Directions (Examples 6-8) In the given histogram, there is survey for the different; family of different income group of a village. Study the graph carefully and answer the questions given below. ssc (1o+2) 2010**

**6. How many families were surveyed?**

(a) 235

(b) 220

(c) 200

(d) 195

**7. What is the total number of family whose daily income is Rs 800 or more?**

(a) 50

(b) 55

(c) 65

(d) 80

**8. What is the percentage of families whose daily income is less than Rs 500?**

(a) 90

(b) 45

(c) 30

(d) 20

**Important Facts**

* If any bar has frequency zero, then no bar will be formed for that class interval.

* In histogram, the minimum and maximum value of interval of bar is called measurement of bars. Frequency density = Frequency of each class (bar)/Number of units of class interval

**(b) Frequency Polygon**

A frequency polygon shows a frequency distribution emphasizing the overall pattern in the data.

In this polygon fragmented categories are denoted an -Y-axis and frequencies are denoted on y-axis.

A frequency polygon can be constructed by two methods i.e., with the help of a histogram and without help of histogram.

**I. Constructions of a Frequency Polygon with the help of Histogram**

The frequency polygon is that type of polygon in which a closed two-dimensional figure of straight line segments joining the mid-points of the top of the bars of a histogram. The first point is located on the x-axis and is placed in the middle of the interval which precedes the first bar of the histogram.

The last point is located on the x-axis in the middle of the interval immediately following the last bar of the histogram.

**Direction (Example 9) Draw a frequency polygon with the given data.**

**9.**

**II. Construction of a Frequency Polygon without help of Histogram**

To draw a frequency polygon with the help of given class intervals and frequency, first of all find the centre-point of each class interval, then indicate these point on x-axis with corresponding frequencies on y-axis. Now join the points according to parameters.

**Direction (Example 10) Draw a frequency polygon with the given data.**

**10.**

**Directions (Examples 11 -14) Given graph shows the yearly premium of an insurance company which is recovered for the insurance of Rs 1000 for different ages. Study the graph and answer the questions given below, ssc (10+2) 2012**

**11, Premium on Rs 10000 for the people of age 27 is**

(a)Rs 460

(b)Rs 45.75

(c)Rs 457.50

(d)Rs 455

**12. Two members of a family are of age 25 yr and 30 yr. What will be the premium for both of them for the insurance of Rs 10000 each?**

(a) Rs 925

(b) Rs 910.60

(c) Rs 876.25

(d) Rs 885

**13.If the person of age 28 yr is replaced by an another person of age 35 yr with an insurance of Rs 1000, then what will be per cent increase in the premium?**

(a) 5%

(b) 4.75%

(c) 5.43%

(d) 6.24%

**14. What will be the premium for a person of age 31 yr for the insurance of Rs 1000?**

(a)Rs 47

(b)Rs 46

(c)Rs 48

(d)Rs 47.75

**Important Facts**

* The surface under the frequency polygon is exactly the same as the surface of the histogram i.e., it represents the same amount of data.

* Frequency polygon can be drawn with freehand. In frequency polygon, for any class, frequency of the unit class-interval is called frequency density.

**Reference Corner**

**Directions (Q.Nos. 1 -4) Study the table and answer the questions. ssc (10+2)2015**

**1.The number of years during which the company has its production less than the average production during 1920-1927 is approximately?**

(a) 4

(b) 2

(c) 3

(d) 6

**2. The average production of steel is**

(a) 74.07

(b) 76.09

(c) 77.10

(d) 75.13

**3. The difference of the production of steel in the year 1923 and 1924 is x% of 1927. Then, the value of xis approximately**

(a) 0.001%

(b) 1%

(c) 0.01%

(d) 0.1%

**4. The ratio of production of steel in the year 1924 and 1925 to that of 1923 and 1927 is**

(a) 2005 : 2077

(b) 2205 : 2007

(c) 2205 : 2077

(d) 2077 : 2205

**Directions (Q. NOS. 5-8) Study the graph and answer the questions. ssc (10+2) 2014**

**5. What was the pass percentage in year 2008?**

(a)75%

(b)78%

(c)33 1/3%

(d)82 6/17%

**6. What was the number of third division in year 2006?**

(a) 59

(b) 120

(c) 60

(d) 140

**7.In which year, did the college have the best result for B.Com.?**

(a) 2007

(b) 2006

(c) Both (a) and (b)

(d) 2008

**8. How many per cent passed in first division in year 2007?**

(a) 16 2/3

(b) 12 1/2

(c) 15 15/19

(d) 11 13/17

**Directions (Q. Nos. 9-13) Study the graph carefully and answer the questions given below. SSC (10+2) 2014**

**9. Number of patients of age between 55 yr to 66 yr, who got admitted to the hospital on that day is**

(a) 6

(b) 4

(c) 24

(d) 8

**10. Total number of patients of age more than 55 yr, who got admitted to the hospital is**

(a) 4

(b) 7

(c) 9

(d) 10

**11. Number of patients of age more than 40 yr and less than 55 yr, who got admitted to the hospital on that day is**

(a)20

(b)30

(c)15

(d)12

**12. Percentage of patients of age less than 45 yr, who got admitted to the hospital on that day is approximately equal to**

(a) 14

(b) 20

(c) 37

(d) 62

**13. About 11% of the patients who got admitted to the hospital on that particular day were of age**

(a) either between 35 yr and 40 yr or between 55 yr and 60 yr

(b) between 60 yr and 65 yr

(c) between 35 yr and 40 yr

(d) between 35 yr and 40 yr and between 55 yr and 60 yr

**Practice Exercise**

**Directions (Q. NOS. 1-5) Study the following graph carefully to answer these questions.**

**1. Number of students in college B in.the year 2008 is what per cent of total number of students in college B in all the years together? (Round off to two digits after decimal.)**

(a) 20.61

(b) 23.79

(c) 21.79

(d) 17.29

**2. What is the average number of students in college A for all the years together?**

(a) 45000

(b) 50000

(c) 52000

(d) 48000

**3. What is the approximate percentage rise in the number of student of college B from 2005 to 2006?**

(a) 8

(b) 12

(c) 4

(d) 15

**4. For which colleges, and in which year was, the per cent rise in number of students from ‘the previous year the highest? ‘**

(a) College A in 2004 and college B in 2005

(b) Only college B in 2004

(c) College A in 2004 anti college B in 2004

(d) College A in 2007 and college B in 2004

**5. What is the ratio between the total number of students in college A in the year 2004, 2006 and 2007 together and-the, total number of students in college B in the year 2003, 2004 and 2008, respectively?**

(a) 35:32

(b) 33:37

(c) 34:31

(d) 32:35

**Directions (Q. Nos. 6-10) Study the following graph and answer the questions that follow.**

**6.What was the respective ratio between the number of candidates qualified in the written test in the year 2002 for admission in institution B and the number of candidates qualified in the written test in the year 2006 for admission to institution A?**

(a) 8:5

(b)7: 4

(c) 7:8

(d) 7 : 5

**7. What was the approximate average number of candidates qualified in the written test for admission to institution B over all the year?**

(a) 4555

(b) 4200

(c) 4160

(d) 4667

**8. In which year, the total number of candidates qualified in the written test for admission to both the institutions together was the second highest?**

(a) 2003

(b) 2004

(c) 2005

(d) 2006

**9. What is the difference between the total number of candidates qualified in written test in the year 2006 for admission to institutions A and B together and the number of candidates qualified in written test in the year 2003, for admission to institution A?**

(a) 5000

(b) 3500

(c) 1500

(d) 5500

**10. What was the total number of candidates qualified in the written test for admission to institution A over all the years together?**

(a) 27000

(b) 26500

(c) 26000

(d) 27500

**Directions (Q. NOS. 11-15) Study the following graph and answer the questions that follow.**

**Number of Candidates Appeared and Passed[in hundred) in a Test from Seven Different Institutions**

**11. What is the difference between the number of candidates appeared in institutions B, C, D and F together and candidates passed from institutions A, E and C together?**

(a) 100

(b) 900

(c) 1000

(d) 540

**12. What is the average number of candidates passed from all the institutions together?**

(a) 700

(b) 490

(c) 350

(d) 675

**13. Number of candidates passed from institutions C and E together is approximately what per cent of the total number of candidates appeared in institutions A and G together?**

(a) 72

(b) 62

(c) 54

(d) 67

**14. From which institution, the difference between the appeared candidates and the passed candidates is maximum?**

(a) B

(b) C

(c) D

(d) F

**15. What is the respective ratio of the number of candidates who got failed from institution B to the number of candidates who have appeared in institution F?**

(a) 2 : 5

(b) 2 : 3

(c) 4 : 3

(d) 1 : 3

**Directions (Q. Nos. 16-19) The following chart represents the number of students of AMS Careers at its Lucknow center who passed the CAT exam or the XAT exam or the CET exam or none of these exams. (Assume that there are no students who passed more than one exam.)**

**16. What was the percentage of students who cleared CAT in 2010?**

(a) 19.50%

(b) 12.65%

(c) 14.28%

(d) 11.76%

**17. What was the percentage of students who succeeded in at least one of the three exams in 2010?**

(a) 82.4%

(b) 82,8%

(c) 82.35%

(d) 83.3%

**18. Which year showed the best result in MBA entrance exams for the institute (in terms of percentage of students who cleared)?**

(a) 2010

(b) 2011

(c) 2012

(d) Cannot be determined

**19. What is the percentage increase in the number of students in 2012 over 2010?**

(a) 30%

(b) 17.64%

(c) 117.6%

(d) 85%

**Directions (Q. NOS. 20-22) The following chart figure shows the production of cars in thousands.**

**20. The ratio of Hindustan Motor’s production in 2011-12 to Honda’s production in 2010-11 is**

(a) 0.66

(b) 1.5

(c) 2

(d) None of the above

**21. For how many companies has there been no decrease in production in any year from the previous year?**

(a) One

(b) Two

(c) Three

(d) Four

**22. How many companies have shown production ,below their average production in 2010-11, but have showed a boy average production in 2011-12?**

(a) One

(b) Two

(c) Three

(d) Four

**Directions (Q. NOS. 23-27) The following is a horizontal bar diagram showing the accidents in which two wheelers are involved with other objects. Study the diagram and answer the questions. ssc (10+2) 2012**

**23. The percentage of accidents in which pedestrians and cyclists are involved is**

(a) 60%

(b) 20.4%

(c) 24%

(d) 6%

**24.The percentage by which the accidents involving buses is less than the accidents involving tanker lorry is**

(a) 40%

(b) 28%

(c) 6%

(d) 4%

**25.The difference in percentage between the accidents involving two wheelers and other objects is respectively.**

(a) 54% more

(b) 54% less

(c) 77% more

(d) 77% less

**26. 60% of the accidents happened due to**

(a) two wheelers, cars, buses and stationary vehicles

(b) two wheelers, cars, buses and tanker lorry

(c) cars, buses, tanker lorry and pedestrians

(d) cars, tanker lorry, bicycles and stationary vehicles

**27. If the data of the bar diagram is represented by a pie chart and the angle of a sector of the pie chart is 36°, then this sector represents the accidents involving**

(a) buses

(b) stationary vehicles

(c) pedestrians

(d) bicycles

**Directions (Q. Nos. 28-32) In the histogram below marks obtained by 45 students of a class is given. Study the histogram and answer the questions given below.**

**28.How many students got less than 10 marks?**

(a) 2

(b) 10

(c) 1

(d) 4

**29.How many students got more than 30, but less than 40 marks?**

(a) 3

(b) 4

(c) 5

(d) 6

**30.How many students got 50 or more marks?**

(a) 9

(b) 10

(c)11

(d) 16

**31.If the minimum passing marks are 30, then how many students failed in the examination?**

(a) 2

(b) 6

(c) 18

(d) 20

**32.If the minimum passing marks are 30, then what is the percentage of passed students?**

(a) 75%

(b) 60%

(c) 50%

(d) 40%

**Answers**

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