SESSION 12: GRAPHING PROBLEMS - Mindset Learn

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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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. 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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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 percentage of 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:

Drink Coke Fanta Sprite Water Coke Light Fruit Juice Total

Frequency 9 4 6 7 6 3 35

? 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

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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 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 merely show a possible trend.

Example

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Mathematical Literacy Grade 11

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

No. of People

420

400

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

45

40

19

20

0

Sub 2 hours

413

61 > 2 hours

Females Males

Finishing Time

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Amount

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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.

R 35 000 R 30 000

Expenditure and Income Incurred in the MTB Race

R 32 280

R 25 000

R 20 000 R 18 000 R 15 000

R 14 000

R 15 000

R 10 000

R 5 000

R 0 Rental of field & clubhouse

R 2 000

R 3 500

Rental of Rental of start Payment for

marquee

banner

DJ

R 4 800

Drinks for watering stations

Expenditure Items

R 6 000

R 5 200

Rental of fencing for start and

finish

Payment for Security Company

Sponsorship

Entry fees

Income Items

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:

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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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