Pictogram, Bar Graph, Pie Chart, Line graph
Pictogram:
1. A pictogram is a chart that uses pictures to represent data.
2. Pictorial symbol for a word or phrase.
3. In a pictogram, a figure is used to represent a category.
4. An advantage of a pictogram is that it is more colorful and appealing while a disadvantage is that it is difficult to use icons to represent exact values.
5. A pictogram is most suitable when the data has to be presented in a lively and interesting manner and when the data do not include values that require a fraction of the icon to be used.
Bar Graph:
1. The bars in a bar graph must be of the same width.
2. The space between the bars allows for ease of distinction between each category.
3. An advantage of a bar graph is that the data sets with the lowest and the highest frequencies can be easily identified while a disadvantage is that if the frequency axis does not start from 0, the displayed data may be misleading.
4. A bar graph is most suitable when we want to compare the data sets and when we are interested to know the exact numerical values.
A pie chart is most suitable when we want to show the relative size of each data set in proportion to the entire data set.A line graph is most suitable when we want to show trends over a period of time.
Q.1. What is a graph?
Ans: A special representation of data to arrange those to be useful is called a graph.
2. Why graphs are drawn?
Ans: To get a visual representation.
3. What is called numbers arranged in the equal interval?
Ans: Organized data
4. In histogram what is the shape of columns?
Ans: Rectangular
5. What is a census?
Ans: Calculating the population of a country is called a census.
6. What is a tally?
Ans: A special sign "I" is used to express the number of given data is called tally.
7. Write the formula to find the average of data.
Ans: Average = Sum of data / Number of data
Q.6. The bar graph illustrates the results of a survey conducted on shops in a housing estate.
i) Find the total number of workers employed in the housing estate.
Ans: 53
ii) Express the number of shops hiring 3 or more workers as a percentage of the total number of shops in the housing estate.
Ans: 50%
iii) Suggest why some shops employ more workers than others.
Q.2. The graph shows the number of candidates who sat for an examination in each year from 2007 to 2012.
i) State the number of candidates who sat for the examination in 2009.
Ans: 950
ii) State the number of candidates who failed the examination in 2012.
Ans: 500
iii) Express the number of candidates who failed the examination in 2012 as a percentage of the total number of candidates who failed the examination in the six years.
Ans: 20 20/49
iv) Comment on the trend in the percentage of successful candidates throughout the six years. Provide a reason for this trend.
Pie Charts
Q.1. A survey is conducted to find out which of the four ice-cream flavors, chocolate, yam, mango, and vanilla, the students in a class prefer. The pie chart shows the results of the survey.
i) If one-quarter of the class prefers yam, state the angle of the sector that represents this information.
ii) Find the angle of the sector that represents the number of students who prefer vanilla.
iii) If 5 students prefer mango, find the total number of students in the class.
iv) Express the number of students who prefer vanilla as a percentage of the total number of students in the class.
Solution:
i) If one-quarter of the class prefers yam, state the angle of
the sector that represents = 90⁰
ii) Sum of angles = 360⁰
Total number of students who prefer chocolate, yam, mango
= ( 120⁰ + 90⁰ + 50⁰)
= 260⁰
The number of students who prefer vanilla = (360 - 260)
= 100⁰ Ans.
iii) If 5 students prefer mango,
so the total number of students in the class = 360/50 X 5
= 36 Ans.
Q.2. The pie chart shows the sources of revenue of a publishing company.
i) Express the revenue the company earns from newspapers as a percentage of the total revenue of the company.
ii) Express the revenue of the company earns from magazines as a percentage of the total revenue of the company.
iii) If the revenue the company earns from books is 17.5 % of the total revenue of the company, find the value of x.
Solution:
i) 180⁰/360⁰X 100%
= 50% Ans.
ii) 72⁰/360⁰ X 100%
= 20% Ans
Q.3. The pie chart shows the nutritional composition of a food product.
i) Calculate the value of x.
ii) Express the amount of fat as a percentage of the components of the food product.
iii) Given that a food product contains 120 g of carbohydrates,
calculate the mass of the food product.
Solution:
i) 144⁰ + 9x⁰ + 2x⁰ + x⁰ = 360⁰
12x⁰ = 360⁰ - 144⁰
= 216⁰
x⁰ = 18⁰
x = 18
ii) Angle of sector representing the amount of fat in the food product
= 2 x 18⁰ = 36⁰
Required percentage = 36⁰/360⁰ x 100%
= 10%
iii) The angle of the sector representing carbohydrates is 144⁰ and this constitutes 120 g.
Mass of the food product = 360⁰ / 144⁰ x 120
= 300 g
Q.4. The pie chart shows the composition of a jar of fruit punch.
i) Find the value of x.
ii) Express the amount of apple juice in the fruit punch as a percentage of all the components in the fruit punch.
iii) Given that a jar of fruit punch contains 759 ml of cranberry juice, find the amount of fruit punch in the jar.
Solution:
i) 237.6⁰ + 4x⁰ + 2x⁰ = 360⁰
or, 6x⁰ = 360⁰ - 237.6⁰
or, x⁰= 20.4 Ans.
ii) Angle of sector representing the amount of apple juice in the fruit punch = 4x⁰
= 4 x 20.4
= 81.6
Required percentage = 81.6/360 x 100%
= 22.67% Ans.
iii) The angle of the sector representing cranberry juice is 237.6⁰
and this contains 759 ml.
Q. 5. The pie chart shows the distribution of students and teachers in a school.
a) If there are five times as many female students as teachers in the school,
find the angle of the sector that represents the number of teachers in the school.
b) If there are 45 teachers in the school,
i) find the number of female students in the school,
ii) find the number of male students in the school.
c) If 2/3 of the teachers are women, express the number of females in the
school as a percentage of the total school population.
Q.6. The monthly expenditure of Raj is presented in a 3-dimensional pie chart
and a 2-dimensional pie chart respectively.
i) Based on the 3-dimensional pie chart, which item does Raj spend the most on?
ii) Based on the 2-dimensional pie chart, which items does Raj spend the most on?
iii) Suggest a reason to explain the discrepancy between your answer in (i) and (ii)
Q.7. The pie chart shows Devi's monthly expenditure.
If the amount she spends on clothes is times as much as that she spends on food,
i) express the amount she spends on food as a percentage of that she saves,
Ans: 40%
ii) find her annual income.
Ans: $48,000
Q.8. The pie chart shows the cost breakdown of a holiday.
a) Find the percentage of the cost that was spent on
i) food Ans: 80%
ii) hotel
b) If 15% of the total cost was spent on travel, find the value of x. Ans: 20.7
Q. 9. Climate change is defined as significant variations in the statistical observations of the weather conditions, which occur over an extended period of time.
a) An indication of climate change is the overall increase in the annual mean surface temperature. Studies show that the annual mean surface temperature in Singapore has increased from 26.8⁰C in 1948 to 27.6⁰C in 2011. Find the percentage increase in the annual mean surface temperature in Singapore from 1948 to 2011, giving your answer correct to 2 decimal places.
b) One of the contributors to climate change is greenhouse gas emissions. Singapore's emissions were 41 million tonnes (MT) in 2005. Singapore's Business-As-Usual (BAU) emissions are expected to reach 77.2 MT in 2020. The pie chart shows a projection of Singapore's BAU emissions for the year 2020 for various sectors.
Source: National Climate Change Secretariat, Prime Minister's Office (Singapore)
Note: Others include waste, water, and other electricity use.
i) Which of the above accounts for the majority of Singapore's projected emissions in 2020? Find the amount of emissions contributed by that sector.
ii) Give two reasons for the likely increase in emissions from 2005 to 2020.
c) Find out some measures that have been put in place by the Singapore government to reduce emissions and mitigate the effects of climate change.
Line Graphs:
* A-line graph is preferred when we want to observe a rising or falling trend in a set of data over a period of time. To obtain a line graph, we can plot the points on graph paper and connect each successive point by line segments.
* An advantage of a line graph is that intermediate values can be easily obtained while disadvantage values may not be meaningful.
* A-line graph is most suitable when we want to show trends over a period of time.
Problem involving a Line Graph:
Q.2. The line graph shows the rubber consumption of the automobile industry in a country from January to May of a particular year.
i) In which month was the rubber consumption the lowest?
ii) Using data from the line graph, construct a table showing the rubber consumption over the five months.
iii) Calculate the percentage increase in rubber consumption from February to March.
iv) Suggest a reason for the increase in rubber consumption from February to March.
Solution:
i) The rubber consumption was the lowest in May.
iii) Percentage increase in the rubber consumption from
February to March = 200-155/155 X 100%
= 29%
iv) The increase in rubber consumption from February to March may be caused by an increase in sales as more rubber tires were needed for the production of more vehicles.
Q.2. The line graph shows the number of total road casualties in each year from 2005 to 2009.
i) In which year was the number of fatal road casualties the highest?
ii) Using data from the line graph, construct a table showing the number of fatal road casualties over the five years.
iii) Find the percentage decrease in the number of fatal road casualties from 2008 to 2009.
iv) Suggest a reason for the decrease in the number of fatal road casualties from 2008 to 2009.
Solution:
i) The number of fatal road casualties was the highest was 2008.
ii)
Year 2005 2006 2007 2008 2009
Number of
fatal road 172 190 214 221 184
casualties