20 LO4 Analysis and Interpretation of Data

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Grade 12 Mathematical Literacy

LO4 Analysis and interpretation of data: Criticallyanalyse and interpret data

1. Inflation is the phenomenon where the purchasing value of the

rand decreases, which results in the price of a product increasing.In order to measure inflation a ‘base year’ is used tocompare the price of goods in the base year to theprice of goods in the year in question. A ‘basket’ of goods and services are identified and used for thecalculation of inflation.

In January 2000 a basket of goods and services cost R200. Ayear later the same basket of goods and services cost R211. In2002 the same basket of goods and services cost R232. Look atthe table below, copy and complete the table by determining theinflation rate per year and since 2000.

Date Costper basket

Inflation rate per year Inflation rate since 2000

January2000

R200 - -

January

2001

R211 %,55

1

100

200

200211=×

−%,55

1

100

200

200211=×

−

January2002

R232 %,9591

100

211

211232=×

−%16

1

100

200

200232=×

−

January2003

R256

January2004

R279

January2005

R299

January2006 R306

January2007

R326

Maths & Science Marketing




2. The table on the right shows thereal cost of a ‘sweetie pie’ over thelast five years. Copy and competethe table, determining the annualpercentage increase.

3. Neville, a traffic officer, earned R6 000 in January 2000. Calculatehis salary in 2007 if:

3.1 His salary increased by the CPI of 6% per annum.

3.2 His salary increased by 5% for two years,by 7,5% for the next two years, and by 8%per year after that.

3.3 The inflation rate over the seven yearsaveraged at 7,2%. What effect would thishave on Neville’s spending power?


Year Price %Increase

2000 R0,85

2001 R0,95

2002 R1,05

2003 R1,122004 R1,25

2005 R1,39

2006 R1,55

2007 R1,85




4. The table below shows a record of profit made by AllbestEngineering over a seven year period.

4.1 Copy and complete the table bydetermining the annual growth per year and the profit index. Make useof the following formulae.

Annual growth:1

100×

year previousinProfit

year previousinProfit-year currentinProfit

Profit index: 100×

year baseinProfit

year currentinProfit

Year 2000(baseyear)

2001 2002 2003 2004 2005 2006

Profit(Rmillion)

1 2 4 6 8 11 15

AnnualGrowth - 100%

Profit

Index 200

4.2 What can you deduce about the business from the abovetable?





5. Smith Company drew up the following three graphs to representtheir profits over the last three years. Study the graphs andanswer the questions that follow.

5.1 Take into account that the profit for all three graphs is the sameand explain how the graphs differ.

5.2 Explain the pattern that is shown by the annual profit.

5.3 Which graph would you recommend to the managing director

should be used at a meeting of the shareholders? Explain your answer.





6. The following table represents the number of children in a class,the number of children who eat sweets and the number of childrenin the class who required fillings during the year. Study the tableand answer the questions that follow.

Number of children per class

35 43 35 38

Number whoeat sweets 15 38 32 26

Number of fillings 16 35 29 26

6.1 Assume that you work for the Dental Association of SouthAfrica and draw an accurate, but biased statistical diagram thatreflects your viewpoint.

6.2 Explain why you chose to do your diagram in the manner inwhich you did it.

6.3 Assume that you are the spokesperson for a sweetmanufacturer and draw an accurate, but biased statistical

diagram that reflects your viewpoint.

6.4 Explain why you chose to do your diagram in the manner inwhich you did it.





7. The following statistical diagrams appeared in a company’sfinancial reports. Study the diagrams and critically analyse eachone.

7.1

7.2





7.3

7.4





ANSWERS

1.

Date Cost

per basket

Inflation rate per year Inflation rate since 2000

January2000

R200 - -

January2001

R211 %,551

100

200

200211=×

−%,55

1

100

200

200211=×

−

January2002

R232 %,9591

100

211

211232=×

−%16

1

100

200

200232=×

−

January2003

R256 10,34% 28%

January2004

R279 8,98% 39,5%

January2005

R299 7,17% 49,5%

January2006

R306 2,34% 53%

January2007

R326 6,54% 63%





2.

3.1 and 3.2

Year 3.1: 6% 3.2: 5%, 7,5%, 8%

2000 R6 000 R6 000

2001 R6 000 x 1,06 = R6 360 R6 000 x 1,05 = R6 300

2002 R6 741,60 R6 615

2003 R7 146,10 R7 111,13

2004 R7 574,86 R7 644,46

2005 R8 029,35 R8 256,12

2006 R8 511,11 R8 916,502007 R9 021,78 R9 2629,82

3.3 Neville’s spending power, taking inflation into account, woulddecrease each year if he received the 6% payincrease. He would be able to buy less eachyear, which would mean that although his salarywas increasing, he would be in a worse positionfinancially than before 2000. Taking the other option into account, the first two years would put

Neville in a similar position as the 6% increasewould. He would be in a better position after that,although he could not make up for the poor twoyears before that when he was in a worseposition financially.


Year Price % Increase

2000 R0,85 -

2001 R0,95 %,7611

1

100

85

8595=×

−

2002 R1,05 10%

2003 R1,12 6,67%

2004 R1,25 11,67%

2005 R1,39 11,2%

2006 R1,55 11,51%

2007 R1,85 19,35%




4.1

Year 2000(baseyear)

2001 2002 2003 2004 2005 2006

Profit(Rmillion)

1 2 4 6 8 11 15

AnnualGrowth - 100% 100% 50% 33,33% 37,5% 36,36%

ProfitIndex 200 400 600 800 1100 1500

4.2 Although the profit index grows each year, the annual growthpercentage per year is decreasing. The business is not doing as

well as it did in 2001 and 2002. They need to revise their strategies in order to improve their business or they may run intotrouble financially in a few years time.

5.1 Although the profit shown by the graphs is the same, the y-axisfor each graph is different. Option 1’s y-axis scale has morepoints than Option 2 or Option 3. Option 3’s y-axis scale hasless points that Option 1 or Option 2. By breaking the y-axis atthe base it implies that there are missing points on the graph,

giving the impression that the profit is higher than it actually is.

5.2 The profit increased by the same amount each year.

5.3 Option 3 implies a bigger profit because of the broken y-axis,but Option 1 looks like there is a bigger profit because the y-axis has more points. I would show the shareholders Option 1.





6.1 Possible diagram:

Effect of eating sweets on learners dental

health

0

5

10

15

20

25

30

35

40

45

50

Class 1 Class 2 Class 3 Class 4

Class

N u m b e r o f l e a r n e r s

Number in class

Number who eat

sweets

Number of fillings

6.2 The line graph emphasises the number of learners who eatsweets and the number of learners who require fillings. Thegraph is elongated, which implies that it may be more than it

actually is.

6.3 Possible diagram:

Number of learners who eat sweets

0

10

20

30

40

50

Class 1 Class 2 Class 3 Class 4

Class

N u m b e r

l e a r n e r s

Number in class

Number who eat

sweets

Number requiring

dentistry





6.4 The line graph emphasises the number of learners in the classand the number of learners who eat sweets. The graph isflattened in order to imply that there aren’t many who havefillings.

7.1 There is no scale on the y-axis, so it is not possible todetermine what the profit actually was.Although it appears that the profits haveincreased, it is not possible to determine theactual point, so it is not possible to concludeanything about the profits except that they appear to haveincreased.

7.2 Using different colours and different thicknesses for the

different years implies that in the sales in the last year weremuch greater than in previous years.Without a scale on the y-axis it is not possibleto determine just how much thesales have increased by. Onceagain, this is a deceptive graph.

7.3 The different colours and the different sizes of the imports for the different years imply that the exports in the last year weremuch greater than in the previous years.Without the scale on the y-axis, or any other relevant information, this graph is once againdeceptive and gives no real ideal of the real values of theimports.

7.4 This graph has no dates, no amounts, no percentages or anyother relevant information. It appears that the shareholdershave received large payout, but there is nothing to compare thesections to. It does not say if the different colours are all

assigned to the shareholders, or whether thepie chart represents the profit and the differentsections represent the various payouts to bemade, such as taxation or general reserves.This is another deceptive graph that as it does not containenough information.


20 LO4 Analysis and Interpretation of Data

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