Arithmetic - Data Interpretation

Data Interpretation

Figure 1: Data interpretation involves analyzing data presented in tables, bar graphs, line graphs, and pie charts.

1. Introduction

Data Interpretation questions are based on the information given in tables and graphs.

CLASSIFICATION OF DATA INTERPRETATION

• Tables: Logical listing of quantitative data in vertical columns and horizontal rows.
• Bar Graphs: Rectangles of uniform width representing magnitudes.
• Line Graphs: Show how a quantity changes over time.
• Pie Charts: Pictorial representation using sectors of a circle.

Degree of any component = (Component value / Total value) × 360°

1% of total value = 3.6°

REMEMBER

• Average = Sum of all items / Number of items
• % change = (Change / Original) × 100
• In pie charts, the angle of each sector is proportional to the value it represents.

2. Graph Types

BAR GRAPHS

• Simple Bar Graph: One dependent variable
• Sub-divided Bar Graph: Break down of total into components
• Multiple Bar Graph: Multiple inter-related variables

LINE GRAPHS

• Used to show how a quantity changes over time
• If line goes up → quantity increasing
• If line goes down → quantity decreasing
• If line is horizontal → quantity not changing

PIE CHARTS

• Numerical data represented by non-intersecting adjacent sectors of a circle
• Sector area proportional to magnitude of data
• 1% of total = 3.6° at the centre

3. Exercise (Questions 1-10)

Q1. What is the total marks obtained by Meera in all subjects?

• (a) 448
• (b) 580
• (c) 470
• (d) 74.67

Answer: (c) 100 + 80 + 50 + 90 + 90 + 60 = 470

Q2. What is the average marks obtained by seven students in History?

• (a) 72.86
• (b) 27.32
• (c) 24.86
• (d) 29.14

Answer: (a) (80+70+70+60+90+60+80)/7 = 72.86

Q3. How many students have got 60% or more marks in all subjects?

• (a) One
• (b) Two
• (c) Three
• (d) Four

Answer: (b) Only Kunal and Soni

Q4. What is the overall percentage of Kunal?

• (a) 64
• (b) 65
• (c) 75
• (d) 64.24

Answer: (c) (90+70+60+90+70+70)/6 = 75%

Q5. In which subject is the overall percentage the best?

• (a) Maths
• (b) Economics
• (c) History
• (d) Science

Answer: (a) Maths has highest overall marks

Q6. If the expenditure of Company B in 2000 was ₹200 crores, what was its income?

• (a) 240 crores
• (b) 220 crores
• (c) 160 crores
• (d) Cannot be determined

Answer: (a) 200 × 120/100 = ₹240 crores

Q7. If the income of Company A in 2002 was ₹600 crores, what was its expenditure?

• (a) 360 crores
• (b) 480 crores
• (c) 375 crores
• (d) Cannot be determined

Answer: (c) 600 × 100/160 = ₹375 crores

Q8. If the income of Company B in 1998 was ₹200 crores, what was its profit in 1999?

• (a) 21.5 crores
• (b) 153 crores
• (c) 46.15 crores
• (d) Cannot be determined

Answer: (d) Cannot be determined

Q9. If the incomes of the two companies in 1998 were equal, what was the ratio of their expenditure?

• (a) 1:2
• (b) 26:27
• (c) 100:67
• (d) Cannot be determined

Answer: (b) 100/135 : 100/130 = 26:27

Q10. What is the percent increase in percent profit for Company B from 2000 to 2001?

• (a) 75
• (b) 175
• (c) 42.86
• (d) Cannot be determined

Answer: (a) (35-20)/20 × 100 = 75%

4. Exercise (Questions 11-20)

Q11. What is the average percentage growth of sales of Assembled PCs for the given years?

• (a) 30
• (b) 20
• (c) 40
• (d) 35

Answer: (d) (20+25+25+50+55)/5 = 35%

Q12. If Branded PCs sold in 1996 were 100000, how many Branded PCs were sold in 1999?

• (a) 202800
• (b) 156000
• (c) 234000
• (d) 300000

Answer: (d) 100000 × (130/100) × (100/100) × (100/100) × (100/100) = 300000

Q13. What is the difference between total Branded and total Assembled PCs sold for the given years?

• (a) 75000
• (b) 750000
• (c) 175000
• (d) Cannot be determined

Answer: (d) Cannot be determined

Q14. In which year is the difference in the growth between Branded and Assembled PCs lowest?

• (a) 1995
• (b) 1998
• (c) 1999
• (d) None of these

Answer: (d) 1997 has lowest difference (5%)

Q15. For Assembled PCs sale, which year is the percent growth the highest compared to previous year?

• (a) 1999
• (b) 1996
• (c) 1998
• (d) Cannot be determined

Answer: (c) 1998 has 25% growth

Q16. In which period the percentage increase in total internet owners is least compared to earlier period?

• (a) 1997-98
• (b) 1998-99
• (c) 1999-2000
• (d) 2001-02

Answer: (d) 65.56% is the least

Q17. What is the total number of fresh internet owners in the period 2001-02?

• (a) 54900
• (b) 549000
• (c) 990000
• (d) 99000

Answer: (c) (1550000+950000) - (1060000+450000) = 990000

Q18. What is the proportion of Government internet owners to Private internet owners in 1999-2000?

• (a) 13:4
• (b) 13:3
• (c) 3:13
• (d) 4:13

Answer: (b) 520000:120000 = 13:3

Q19. What is the approximate percentage increase in Private internet owners in 2001-02 over 1998-99?

• (a) 5000
• (b) 6000
• (c) 8000
• (d) 4000

Answer: (c) (950000-12000)/12000 × 100 ≈ 8000%

Q20. What is the approximate percentage of Private internet owners in total internet owners in 1998-99?

• (a) 20
• (b) 5
• (c) 10
• (d) 15

Answer: (b) 12000/(230000+12000) × 100 ≈ 5%

5. Exercise (Questions 21-30)

Q21. If the income of Company X in 1998-99 was equal to the expenditure of Company Y in 2001-2002, what was the ratio of their respective profits?

• (a) 13:15
• (b) 6:13
• (c) 13:26
• (d) Cannot be determined

Answer: (b) 30:65 = 6:13

Q22. For Company X, its income in 2001-2002 was equal to its expenditure in 2002-2003. What was the ratio of its respective incomes in these two years?

• (a) 4:5
• (b) 3:4
• (c) 2:3
• (d) Cannot be determined

Answer: (c) 2:3

Q23. For Company Y, in which year is the percent increase in percent profit over previous year the highest?

• (a) 2002-03
• (b) 1999-2000
• (c) 2001-02
• (d) Cannot be determined

Answer: (c) 2001-02 has 66⅔% increase

Q24. In 1997-98, the expenditure of Company X was ₹40 crores. What was its income in that year?

• (a) ₹50 crores
• (b) ₹48 crores
• (c) ₹46 crores
• (d) Cannot be determined

Answer: (b) 40 × 120/100 = ₹48 crores

Q25. What was the difference in the expenditures of the two companies in 1999-2000?

• (a) 10
• (b) 100
• (c) 1000
• (d) Cannot be determined

Answer: (d) Cannot be determined

Q26. In 2002-03 the income of Company Y was ₹128 crores. What was its expenditure in that year?

• (a) ₹80 crores
• (b) ₹64 crores
• (c) ₹48 crores
• (d) Cannot be determined

Answer: (a) 128 × 100/160 = ₹80 crores

Q27. The production of Company AVC in 2000 is approximately what percent of its average production over the given years?

• (a) 300
• (b) 110
• (c) 136
• (d) 18.25

Answer: (b) 360 × 6 / 1970 × 100 ≈ 110%

Q28. For SIO, which year had the highest percent increase or decrease in production from previous year?

• (a) 2001
• (b) 1998
• (c) 2002
• (d) 2000

Answer: (c) 2002 has 4.35% increase

Q29. Which company has less average production in the last three years compared to first three years?

• (a) No company
• (b) CTU
• (c) ZIR
• (d) None of these

Answer: (a) No company

Q30. The total production of the six companies in the first two given years is what percent of that of last two given years?

• (a) 87.08
• (b) 104.55
• (c) 90.40
• (d) 10.62

Answer: (c) 1790/1980 × 100 = 90.40%

6. Exercise (Questions 31-40)

Q31. For ZIR, what is the difference between production in 2002 and 2001?

• (a) 10,00,00,000
• (b) 1,00,00,000
• (c) 10,00,000
• (d) 40,00,000

Answer: (b) (91-90) crore = 1,00,00,000

Q32. For how many companies did the production increase every year from the previous year?

• (a) One
• (b) Two
• (c) Three
• (d) Four

Answer: (c) ZIR, PEN, and SIO

Q33. The production in 2002 is what percent of production in 1996?

• (a) 650%
• (b) 550%
• (c) 325%
• (d) 320%

Answer: (a) 32.5/5 × 100 = 650%

Q34. What is the approximate average production (in lakhs) for the given years?

• (a) 18
• (b) 19
• (c) 20
• (d) 18.5

Answer: (a) 125/7 ≈ 18 lakhs

Q35. Which year had the highest percent increase in production over the previous year?

• (a) 2000
• (b) 1999
• (c) 2002
• (d) 2007

Answer: (b) 1999 has 75% increase

Q36. What is the total marks obtained by Student R in Subjects B, D and E?

• (a) 200
• (b) 138
• (c) 168
• (d) 156

Answer: (b) 54% of 40 + 84% of 50 + 62% of 120 = 138

Q37. What is the average marks obtained by all students in Subject C?

• (a) 56
• (b) 58
• (c) 54
• (d) 70

Answer: (a) 69.66% of 80 ≈ 56

Q38. What is the average percentage of marks obtained by all students in Subject A?

• (a) 73⅔
• (b) 43⅖
• (c) 72⅓
• (d) 48⅗

Answer: (a) (80+55+74+68+75+82)/6 = 72⅓%

Q39. Approximately what is the overall percentage of marks obtained by Q in all subjects?

• (a) 77
• (b) 72
• (c) 78
• (d) 74

Answer: (d) 315.7/425 × 100 ≈ 74%

Q40. What is the total marks obtained by all students together in Subject E?

• (a) 522
• (b) 488
• (c) 445
• (d) 534

Answer: (d) (75+88+62+72+80+68)% of 120 = 534

7. Exercise (Questions 41-50)

Q41. If the income of company C in the year 2000 was 35 lakhs, what was its expenditure in that year?

• (a) 24 lakhs
• (b) 21 lakhs
• (c) 25 lakhs
• (d) Can't be determined

Answer: (c) 35 × 100/140 = ₹25 lakhs

Q42. If, in the year 2001, total expenditure of companies B and C was 48 lakhs, what was their total income?

• (a) 32 lakhs
• (b) 28.6 lakhs
• (c) 34.2 lakhs
• (d) Can't be determined

Answer: (d) Can't be determined

Q43. If, in the year 2000, expenditure of Company C was 32 lakhs, what was the income of the company in the same year?

• (a) 44.2 lakhs
• (b) 44.80 lakhs
• (c) 46.4 lakhs
• (d) 38 lakhs

Answer: (b) 32 × 140/100 = ₹44.80 lakhs

Q44. If the expenditures of Company E in the years 2000 and 2001 were the same, what was the ratio of the incomes in the same years?

• (a) 19:21
• (b) 11:12
• (c) 29:31
• (d) 9:11

Answer: (c) 145:155 = 29:31

Q45. The income of Company D in the year 2000 was 31 lakhs. What was the earned profit?

• (a) 11 lakhs
• (b) 20 lakhs
• (c) 17 lakhs
• (d) 12 lakhs

Answer: (a) Expenditure = 31 × 100/155 = 20. Profit = 31-20 = 11 lakhs

Q46. What is the percentage of students studying science in institute G with respect to total students in institute G?

• (a) 17.20
• (b) 12.70
• (c) 21⅓
• (d) 21⅔

Answer: (d) 182/840 × 100 = 21⅔%

Q47. Out of the total students of institute D, approximately what percentage study Management?

• (a) 6
• (b) 8
• (c) 12
• (d) 10

Answer: (a) 36/650 × 100 ≈ 6%

Q48. The total students studying Arts in A, B and C together is approximately what percent of total students studying Commerce in D, E, F and G together?

• (a) 50
• (b) 45
• (c) 42
• (d) 55

Answer: (a) (125+96+144)/(138+196+212+206) × 100 ≈ 48.5%

Q49. What is the percentage of students studying Engineering in institute C with respect to total students of all institutions studying Engineering?

• (a) 19
• (b) 20
• (c) 18
• (d) 21

Answer: (b) 164/821 × 100 ≈ 20%

Q50. In which institution, the percentage of students studying Commerce with respect to total students is maximum?

• (a) F
• (b) E
• (c) C
• (d) A

Answer: (c) C has maximum percentage of Commerce students

Complete Answer Key

1. (c)	2. (a)	3. (b)	4. (c)	5. (a)
6. (a)	7. (c)	8. (d)	9. (b)	10. (a)
11. (d)	12. (d)	13. (d)	14. (d)	15. (c)
16. (d)	17. (c)	18. (b)	19. (c)	20. (b)
21. (b)	22. (c)	23. (c)	24. (b)	25. (d)
26. (a)	27. (b)	28. (c)	29. (a)	30. (c)
31. (b)	32. (c)	33. (a)	34. (a)	35. (b)
36. (b)	37. (a)	38. (a)	39. (d)	40. (d)
41. (c)	42. (d)	43. (b)	44. (c)	45. (a)
46. (d)	47. (a)	48. (a)	49. (b)	50. (c)