SESSION 12: GRAPHING PROBLEMS - Mindset Learn · 2018-05-01 · SESSION 12: GRAPHING PROBLEMS Key Concepts In this session we will focus on summarising what you need to know about:

Mathematical Literacy Grade 11

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SESSION 12: GRAPHING PROBLEMS Key Concepts In this session we will focus on summarising what you need to know about:

• Bar graphs • Histograms • Pie charts • Line graphs

X-planation 1. BAR GRAPHS Bar graphs are use to display discrete data. Discrete data is when there cannot be fractions of the item being studied, e.g. people, motor cars or countries. In a bar graph the length of the bar corresponds with the frequency of the object. The gap between the bars indicates that each bar represents a separate category of data. There must be a gap before the first bar. The width of each bar must be the same. There are two main types of bar graphs: Single and compound.

a) Single Bar Graphs show one type/group of data. Example:

b) Compound Bar Graphs show more than one group/type of data. These are also

referred to as double bar graphs for two sets of data and multiple bar graphs for more than two sets of data. The two or more bars that are now present can either be next to each other or on top of each other.

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Example

2. HISTOGRAMS Histograms are used to display continuous data. Continuous data is when there can be a fraction of the item being studied, e.g. histogram is also used to represent data that is grouped in intervals. In a histogram the length of the bar corresponds with the frequency of the object. There is no gap between the bars except there must be a gaeach bar must be the same.

Histograms are used to display continuous data. Continuous data is when there can be a fraction of the item being studied, e.g. growth in a year and speed of a vehicle. A histogram is also used to represent data that is grouped in intervals.

In a histogram the length of the bar corresponds with the frequency of the object. There is no gap between the bars except there must be a gap before the first bar. The width of each bar must be the same.


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Histograms are used to display continuous data. Continuous data is when there can be a growth in a year and speed of a vehicle. A

histogram is also used to represent data that is grouped in intervals.

In a histogram the length of the bar corresponds with the frequency of the object. There is p before the first bar. The width of

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Example

3. PIE CHARTS

A pie chart is useful in showing a comparison of how a whole is divided into different categories. The relative size of each piece of the pie represents the whole that that specific category occupies, for example, the comparison between the number of males and females at your school.

Example

A grade 11 class conducts a survey about learners’ favourite drinks from their tuck shop. They summarise their data as follows:

• To calculate the percentage of each type of drink, convert the frequency into a

fraction of the whole and multiply by 100• To calculate the number of degrees for each type of drink convert the frequency

into a fraction of the whole and multiply by 360

A pie chart is useful in showing a comparison of how a whole is divided into different categories. The relative size of each piece of the pie represents the whole that that specific category occupies, for example, the comparison between the number of males and females at your school.

A grade 11 class conducts a survey about learners’ favourite drinks from their tuck shop. rise their data as follows:

Drink Frequency Coke 9 Fanta 4 Sprite 6 Water 7

Coke Light 6 Fruit Juice 3

Total 35

To calculate the percentage of each type of drink, convert the frequency into a fraction of the whole and multiply by 100

the number of degrees for each type of drink convert the frequency into a fraction of the whole and multiply by 360


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A pie chart is useful in showing a comparison of how a whole is divided into different categories. The relative size of each piece of the pie represents the percentage of the whole that that specific category occupies, for example, the comparison between the

A grade 11 class conducts a survey about learners’ favourite drinks from their tuck shop.

To calculate the percentage of each type of drink, convert the frequency into a

the number of degrees for each type of drink convert the frequency

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4. LINE GRAPHS

A line graph is used to show continuous data. It shows the relation between the dependent (y axis) and independent (x axtrends in the data. Clear points need to be plotted and then joined with line segments. It is important to note that only the points plotted are accurate. The lines between the points merely show a possible trend. Example

A line graph is used to show continuous data. It shows the relation between the dependent (y axis) and independent (x axis) variables. These graphs are useful when trying to see trends in the data. Clear points need to be plotted and then joined with line segments. It is important to note that only the points plotted are accurate. The lines between the points

possible trend.


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A line graph is used to show continuous data. It shows the relation between the dependent is) variables. These graphs are useful when trying to see

trends in the data. Clear points need to be plotted and then joined with line segments. It is important to note that only the points plotted are accurate. The lines between the points


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X-ample Questions

Question 1 Study the following and then answer the questions that follow:

Percentage distribution of population aged 20 years and older by highest level of education

Percentage of households with household goods in working order

a) Comment on the graph showing the distribution of education amongst the population

aged 20 years and older. Substantiate your answer by including percentages. (3)

b) In the 2007 census the number of people, in this particular area, that had received a primary school education was 8 000. Determine the number of people who did not receive any schooling in 2007. (3)

c) i) What is the percentage difference between those who had cell phones in 2001and those who had cell phones in 2007? (2) ii) Do think that this percentage has increased again to today? Why? (2)

d) What are the most popular goods? Why do you think that this is so? (2)


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Question 2 A recent survey looked at households in two income groups. This study determined what percentage of monthly income was spent on food, housing and other requirements. The pie charts below represent the findings of this study.

a) What were the monthly incomes of the groups considered? (2) b) What percentage of group 1’s earnings was spent on housing? (2) c) How much was spent on housing by a household in group 2? (2) d) Which group spent the larger amount of money on food? Justify your answer using calculations. (5) Question 3 A mountain bike race was held recently in Kwa-Zulu Natal. The race was sponsored by a big syrup company and so everyone who entered, received a really pretty shirt and a yummy tin of syrup.

a) The bar graph below shows the number of males and females that finished in different time intervals in the race.

Distribution of the Finishing Times of Females and Males

19

6145

413

020406080

100120140160180200

220240260280300320340360380400420

Sub 2 hours > 2 hours

Finishing Time

No.

of

People

Females

Males


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i) Explain why it is not possible to use this information to make a decision about

whether or not the females or males performed better in the race. (1)

ii) Use any method to determine whether or not as a group the females or males

performed better in the race. Presume that everyone who started

the race did indeed complete the race. (6)

b) The chart below shows a breakdown of the items that the organisers of the race had to spend money on, and the total income generated from the race.

i) Was the race financially successful for the organisers? Use calculations to explain

your answer. (5)

ii) The entry fee for the race was R60,00 per person. How many people

needed to enter the race in order for the race organisers to break-even? (5) Question 4 The compound bar graph below shows the percentage of South African children from age seven to thirteen, enrolled in primary schools during 1996 and 2007. Use the graph to answer the questions that follow:

Expenditure and Income Incurred in the MTB Race

R 18 000

R 14 000

R 2 000R 3 500

R 4 800R 6 000

R 5 200

R 15 000

R 32 280

R 0

R 5 000

R 10 000

R 15 000

R 20 000

R 25 000

R 30 000

R 35 000

Rental of field

& clubhouse

Rental of

marquee

Rental of start

banner

Payment for

DJ

Drinks for

watering

stations

Rental of

fencing for

start and

finish

Payment for

Security

Company

Sponsorship Entry fees

Am

ount

Expenditure Items Income Items


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a) What percentage of the 9-year olds was enrolled during 1996? (1)

b) Calculate the percentage increase in enrolment of 10-year-olds from

1996 to 2007. (3)

c) Which age group had:

i) The largest percentage enrolment during 1996 (1)

ii) The smallest percentage enrolment during 2007 (1)

iii) The greatest increase in percentage between 1996 and 2007 (2)

d) If there were 240 000 10-year old children in South Africa in 1996. Calculate the number of 10 year old children enrolled in primary school. (2)

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X-ercise Question 1 The traffic department at Petrusville, (a town between Johannesburg and Durban) along Route 48, has monitored the number of vehicles travelling through the town over a one year period. The following figures were issued:

January

February

March

April

May

June

July

August

September

October

November

December

a) The pie chart below shows the types of vehicles that passed through the town during

the month of December.

Petrusville, (a town between Johannesburg and Durban) along Route 48, has monitored the number of vehicles travelling through the town over a one year period. The following figures were issued:

2007

2007 (Rounded to

nearest hundred-thousand

(Rounded to nearest hundred

2130015 2 100 000

381562 400 000

A 100 000

1251216 1 300 000

158164 200 000

1325214 1 300 000

852156

325155

210548

421588

325682

2255600

The pie chart below shows the types of vehicles that passed through the town during

the month of December.


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Petrusville, (a town between Johannesburg and Durban) along Route 48, has monitored the number of vehicles travelling through the town over a one

2008 (Rounded to

nearest hundred-thousand

2 000 000

300 000

100 000

1 200 000

200 000

1 200 000

The pie chart below shows the types of vehicles that passed through the town during

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i) Calculate how many trucks pas

ii) If you had been asked to draw the pie chart above, how many degrees would you have made the sector that represents the trucks? Show your working to substantiate your answer. Round to the nearest whole degree.

b. i) On the axes provided, draw a double bar graph showing the

between the number of vehicles in 2007 and 2008 that travelled through Petrusville for the first 6 months of each year. Use above, that haRemember to label your graph carefully, inc

ii) Explain the trend that you notice in your bar graph. Give a possible for this.

Question 2 Bathwizz is a company that installs and renovates bathrooms. The general manager had to present the company's earnings for the first three quarters of the year to the company directors. He drew the two graphs below. Use the graphs to answer the follow:

a) What possible trend do you notice with regard to Bathwizz's quarterly income?

b) Calculate the average (mean) monthly income for Bathwizz for the first nine months of the financial year.

c) The general manager wanted to prove to the company directors that Bathwizz's income was increasing and that the company was doing well.

Which graph would be the better one to show to the company directors? Give a reason for your answer.

Calculate how many trucks passed through Petrusville in

If you had been asked to draw the pie chart above, how many degrees would you have made the sector that represents the trucks? Show your working to substantiate your answer. Round to the nearest whole

On the axes provided, draw a double bar graph showing the between the number of vehicles in 2007 and 2008 that travelled through Petrusville for the first 6 months of each year. Use the figures in the table

e, that have been rounded to the nearest hundred thousand. Remember to label your graph carefully, including the axes.

Explain the trend that you notice in your bar graph. Give a possible

Bathwizz is a company that installs and renovates bathrooms. The general manager had to present the company's earnings for the first three quarters of the year to the company directors. He drew the two graphs below. Use the graphs to answer the

What possible trend do you notice with regard to Bathwizz's quarterly income?

Calculate the average (mean) monthly income for Bathwizz for the first nine months

The general manager wanted to prove to the company directors that Bathwizz's income was increasing and that the company was doing well. Which graph would be the better one to show to the company directors? Give a reason for your answer.


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sed through Petrusville in December?

(3)

If you had been asked to draw the pie chart above, how many degrees would you have made the sector that represents the trucks? Show your working to substantiate your answer. Round to the nearest whole

(3)

On the axes provided, draw a double bar graph showing the differences between the number of vehicles in 2007 and 2008 that travelled through

the figures in the table hundred thousand.

the axes. (6)

Explain the trend that you notice in your bar graph. Give a possible reason (3)

Bathwizz is a company that installs and renovates bathrooms. The general manager had to present the company's earnings for the first three quarters of the year to the company directors. He drew the two graphs below. Use the graphs to answer the questions that

What possible trend do you notice with regard to Bathwizz's quarterly income?

(1) Calculate the average (mean) monthly income for Bathwizz for the first nine months

(4)

The general manager wanted to prove to the company directors that Bathwizz's income was increasing and that the company was doing well. Which graph would be the better one to show to the company directors? Give a

(2)

Documents

SESSION 12: GRAPHING PROBLEMS - Mindset Learn · 2018-05-01 · SESSION 12: GRAPHING PROBLEMS Key Concepts In this session we will focus on summarising what you need to know about: