While bar chart are useful for visual representation of categorical and geographical data, data related to time series and frequency distribution is best presented through x-y or line graph. This representation is widely used by newspapers, television, government report, magazines and research papers.
Besides, x-y graph are really very useful for determining trends, rate of change and for illustrating comparison with respect to some time series.
THE TYPICAL DATA SHOWN ON AN X-Y CHART INVOLVES A TIME SERIES
A time series is an arrangement of data on the basis of time, i.e., in chronological order. The time period may be a year, quarter, month, week, days, hours, etc. Time series are extremely essential for the measurement of economic and business performance.
Hence, most data related to economics and business are in the form of time period. In time series data, time( the independent variable) is seen as a discrete variable while the continuous variable being measured to find the other dependent variable.
normally time is taken along the x axis and the dependent continuous variable is taken along the y-axis.
EXAMPLE OF VARIOUS TYPES OF DATA PRESENTATION POSSIBLE THROUGH X-Y CHARTS
Single dependent variable( continuous) graph:
This graphs show changes in a single variable over a period of time.
More than one dependent( continuous) variable graph
In this type of graph, two or more lines are drawn to represent two or more dependent variables.
Graph with two scales
When two continuous variables having different units of measurement have to be shown on the same graph, we used two scale on the graph.
Range graph
For some specific types of data, it is essential to depict the range of the variation of the variable over a period of time. This is depicted using a range graph, which shows with deviation between different values of the variable under consideration.
Band graph
Like a stacked bar chart, the band graph is a line graph used to display the total value of a continuous variable broken up into its different components for each period.
Speed time graph
This is a special case of x-y chat where the respective Axis show the speed of a moving body against time
EXERCISE
Directions for questions 1-5:
Refer to the graph and answer the questions given below.
1. Which month showed the highest absolute difference in the consumer price index(CPI) over the previous month?
(a) March
(b) April
(c) May
(d) July
2. Which month showed the highest percentage difference in the CPI over the previous month?
(a) March
(b) April
(c) May
(d) July
3. For how many months was the CPI was greater than 350?
(a) One
(b) Two
(c) Three
(d) Four
4. In how many months was there a decrease in the CPI?
(a) One
(b) Two
(c) Three
(d) Four
5. The difference in the number of months in which there was an increase in the CPI and number of months in which there was a decrease was:
(a) One
(b) Two
(c) Three
(d) Four
Directions for questions 6-10:
The following graph shows the sales history( units) of the Lux brand of soap. Observe the sales curve carefully and answer the following question.
6. For how many months was the sales value(by units) at its lowest monthly level?
(a) One
(b) Two
(c) Three
(d) Four
7. The ration of the number of months in which there was a decrease to the number of months in which there was no decrease in the sales value was:
(a) 2:9
(b) 2:8
(c) 2:10
(d) None of these
8. The number of months which exhibited a sales volume greater than 12.5% of the overall annual sales volume was:
(a) One
(b) Two
(c) Three
(d) None of these
9. The highest percentage increase was shown in which month?
(a) March
(b) April
(c) September
(d) November
10. The highest absolutely increase was shown in which month?
(a) March
(b) April
(c) September
(d) All of these
Directions for questions 11-17:
Consider the following graph and answer the questions based on it. The graph shows the trend of consumption of metals and plastics in the production of cars between 2007-12.
11. The numbers of years for which the consumption of metal was less than the consumption of plastic over the given time period was:
(a) One
(b) Two
(c) Three
(d) Four
12. The total consumption of plastic(for car manufacturing) divided by the total consumption of metal(for car manufacturing) over the period will give a ration closets to:
(a) 4:3
(b) 5:4
(c) 6:5
(d) 7:4
13. Which item and for which year shows the highest percentage change in consumption over the previous year?
(a) Metal 2010
(b) Plastic 2010
(c) Metal 2009
(d) Plastic 2012
14. For the two data series shown, how many years have shown a decrease in consumption(for both the items individually)?
(a) One
(b) Two
(c) Three
(d) Four
15. The ratio of the highest total consumption in any single year to the lowest total consumption of the two items taken together in any year was equal to;
(a) 5:3
(b) 7:4
(c) 11:6
(d) 11;7
16. Which year showed the highest percentage increase in the total consumption of the two metals?
(a) 2008
(b) 2009
(c) 2010
(d) 2011
17. Which year showed the highest percentage decrease in the total consumption of the two metals?
(a) 2008
(b) 2009
(c) 2010
(d) 2011
Directions for questions 18-23:
Consider the following graph and answer the questions based on it.
18. At what ages are the requirements of calories for baby boys and baby girls equal?
(a) 2 months
(b) 4 months
(c) 8 months
(d) 2 months and 8 months
19. The difference between the calorie requirement for baby boys and baby girls at the age of 6 months is approximately equal to:
(a) 300 calorie
(b) 250 calorie
(c) 400 calorie
(d) 200 calorie
20. If in a family there are four baby boys aged 4, 6, 8 and 12 months respectively, and three baby girls aged 2, 8 and 16 months respectively, then what is the total calorie requirement per day for the babies in the family?
(a) 12100
(b) 12250
(c) 12400
(d) None of these
21. For the previous question, if the baby girl aged 16 months goes away, what is the percentage change in the calorie requirement per month for the family?
(a) 16.3%
(b) 17.4%
(c) 14.3%
(d) 12.2%
22. For the Previous questions, if the great doctor Raju informs Ravi that the graph have got mixed up and what is shown for the baby boys is for the baby girls and vice versa, then the answer for question 20 would have been:
(a) 12100
(b) 12250
(c) 12400
(d) None of these
23. It can be inferred from the graph that in general, calorie requirement for baby boys and baby girls:
(a) are quite different at all ages.
(b) are similar Till the age of 17 months.
(c) reaches a peak value at the same age.
(d) increase at nearly the same rates in the age of 13.
Directions for questions 24-26:
Consider the following graph and answer the questions based on it.
24. The percentage increase in the sales of footwear between 2010 and 2011 was:
(a) 20%
(b) 30%
(c) 40%
(d) 50%
25. In 2011, if 20% of the footwear sold within the country had been additionally exported at the local price, the percentage increase in export income in the period 2010 to 2011 would have been:
(a) 20%
(b) 30%
(c) 40%
(d) 50%
26. If the sales of the footwear had touched ₹80 crore in 2012, the average annual percentage growth of footwear for the two year period 2010 to 2011 would have been(approximately)?
(a) 50%
(b) 75%
(c) 80%
(d) 90%
Directions for questions 27-29:
The following graph gives information about the number of washing machines produced by HLL.
Answer questions based on the graph.
NOTE: Figures for 2011 are estimated figures. also, assume that everything produced is sold in the same year.
27. What was the value of each machine in 2007?
(a) ₹20,000
(b) ₹83,33.3
(c) ₹2000
(d) ₹833.3
28. What was the percentage drop in the production of the number of Machines from 2008 to 2009?
(a) 20%
(b) 25%
(c) 27%
(d) 32%
29. What was the difference in the value for machine between the years 2007 and 2010?
(a) ₹2000
(b) ₹5000
(c) ₹4000
(d) None of these
Directions for questions 30-32:
Use the following graph showing the Railway finances for the year 1997-98 to 2004-05, answer the questions given.
30. The difference between the gross traffic receipt and the total working expenses was highest during which of the following years?
(a) 1997-98
(b) 2001-02
(c) 2002-03
(d) 2004-05
31. By what percent did gross traffic receipt increase between 1997-98 and 2004-05?
(a) 38%
(b) 124%
(c) 133%
(d) 138%
32. Between the year 1997-98 and 1999-00, ratio of increase in gross traffic receipt and total working expenses are was:
(a) 5:3
(b) 3:5
(c) 2:3
(d) None of these
Directions for questions 33-35:
Study the graph carefully and answer the given questions
33. The highest percentage growth in total revenue was recorded in:
(a) 2000-01
(b) 2001-02
(c) 2002-03
(d) 2004-05
34. In which year what’s the net profit as a percentage of gross revenue at it second highest level?
(a) 2004-05
(b) 2005-06
(c) 2006-07
(d) None of these
35. For which of the following years was the trend of gross revenue net profit/ loss dissimilar?
(a) 2001-02
(b) 2002-03
(c) 2003-04
(d) 2004-05
Directions for questions 36-37:
Observe the given graph and answer the following questions.
36. The minimum difference between day and night temperature is:
(a) 9.5 degrees
(b) 11.5 degrees
(c) 9.7 degrees
(d) none of these
37. The highest ratio of the night to day temperature is for:
(a) 1st May
(b) 3rd May
(c) 4th May
(d) none of the above
Directions for questions 38-39:
Study the graph carefully and answer the given questions. Assume that the curve between any two years marked on the graph is a straight line and the difference between any two years can be got by interpolation. Beyond 2003 the values go up to 2005 and are the projected values for 2004 and 2005.
38. In 1963, the percentage of HBS students who are engineers was about:
(a) 20%
(b) 25%
(c) 30%
(d) 35%
39. Which was the first year when more than 200 students was studying in a batch at HBS?
(a) 1973
(b) 1978
(c) 1983
(d) 1985
Directions for question 40:
The following graph give the movement of a car with respect to time. ( assume that the speed dimension only y axis is marked at every 10 kmph and there is uniform acceleration between hours)
Find the average speed of the car(in kmph):
(a) 36.28
(b) 34.28
(c) 33.57
(d) None of these
ANSWER:
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SOLUTION:
1 & 2. Visually clear that it is April.
3. April and July-Two.
4. The CPI decreased in March and May.
5. The CPI increased in 3 months ( April, June and July) when it is decrease in 2 months ( March and May). Hence, the required answer is 3-2=1.
6. The sales value was at 7000 for 3 months viz. June, July and August.
7. Only 2 months out of 11 have shown a decrease. hence, 2:9.
8. The total sales volume was 97000. 12.5% of this value would mean 1/8th of this value, i.e. more than 12000. this has never occurred during this time.
9. September shows the highest growth and the least initial value. hence, highest percentage increase.
10. March, April and September also and increase of thousand units( which is the highest increase during the period shown).
11. Visually seen as 4.
12. 145:115=29:23 is closest to 5:4
13. Metals in 2009 is more doubling over it’s 2008 value.
14. 2008 is the only year which satisfies the condition.
15. 55 in 2010 to 30 in 2008. gives 11:6 as the answer.
16. 50% 2002.
17. 33.33% between 2007 to 2008.
18. Visually clear that the graph are equal at the age of 2 and 8 months.
19. The required answer=1700-1450=250 calories.
20. Add all the values to get 12250.
21. The required change will be 2000/12250=16.3%
22. Reverse the calculation for question 20 and get 12500 as the total calorie requirement per day.
23. It can be seen that two lines move differently with respect to each other and do not follow any common pattern. hence, option A is correct.
24. 10/25=40%
25. Exports would have increased by 20% of the footwear’s value, i.e. by 7 on 35-20%.
26. Solve through options. When you try with 80%, you get 35+80% of 25=45+80% of 45=81. Hence the answer is just below 80%
27. 10 crore/ 12000.
28. 25000 to 17000.
29. 8333.33-3333.333=5000
30. Visually see the next revenue line to be maximum for 2002-03.
31. The required ratio is 2900/ 2100.
32. 300/500
33. Visually seen as 2004-05.
34. 2005-06 is the highest and 2006-07 is the second highest.
35. Visually seen that the gross revenue decreases in 2003-04 but the net profit has increased.
36. 9.5 for 4th of May.
37. This ratio depends on the difference between the two temperatures on a single day as well as on the day temperature of the same day. The lower the difference, the higher the ratio. Also, the data given is such that the Day temperatures are in the same range, hence the effect of the same on the ratio will be minimal. For solving this question, find out the days which need to be checked and compare the ratios between those days only. 4th of May will give the highest ratio required, since the difference is the lowest on that day.
38. Approximately 40 auto 160=25%.
39. Visually checking the options, we get 1978 as the answer.
40. The average speed will be given by the ratio of Total distance by the total time.
The distance covered in any hour will be given by the average speed of the hour.
Distance covered in the first hour=(20+0)/2=10km
Distance covered in the second hour=20kmhr=20km
Distance covered in the third hour=(20+40)/2=30km
Distance covered in The Fourth Hour=(40+60)/2=50km
Distance covered in the fifth hour=(60+50)/2=55km
Distance covered in the sixth hour=50km
Distance covered in the seventh hour=(50+0)/2= 25 km
The required average speed= 240/7=34.28km/hr