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The Republic of South Africa (RSA) conducts household censuses to collect information - NSC Mathematical Literacy - Question 4 - 2019 - Paper 2

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The Republic of South Africa (RSA) conducts household censuses to collect information. The next census will take place in 2021. Census information regarding househo... show full transcript

Worked Solution & Example Answer:The Republic of South Africa (RSA) conducts household censuses to collect information - NSC Mathematical Literacy - Question 4 - 2019 - Paper 2

Step 1

Determine the percentage increase in the total number of households from 1996 to 2011.

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Answer

To find the percentage increase in the total number of households from 1996 to 2011, we use the formula:

ext{Percentage Increase} = rac{ ext{New Value} - ext{Old Value}}{ ext{Old Value}} \times 100

Substituting the values:

extPercentageIncrease=14.5extmillion−8.7extmillion8.7extmillion×100=5.8extmillion8.7extmillion×100≈66.67% ext{Percentage Increase} = \frac{14.5 ext{ million} - 8.7 ext{ million}}{8.7 ext{ million}} \times 100 = \frac{5.8 ext{ million}}{8.7 ext{ million}} \times 100 \approx 66.67\%

Step 2

State which household size EACH of the following terms: (a) Increased every year, but only by a small percentage.

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Answer

The household size which increased every year, but only by a small percentage, is 'One'.

Step 3

State which household size EACH of the following terms: (b) Remained constant in every census from 1996 to 2011.

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Answer

The household size that remained constant in every census from 1996 to 2011 is 'Four'.

Step 4

Verify, showing ALL calculations, whether this statement is CORRECT.

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Answer

To verify the statement about the decrease in the number of households with five or more persons: From the data, in 2001, households with five or more persons were 33% of 10.8 million:

extHouseholdsin2001=0.33×10.8 million=3.564 million ext{Households in 2001} = 0.33 \times 10.8 \text{ million} = 3.564 \text{ million}

In 2011, households with five or more persons were 25% of 14.5 million:

extHouseholdsin2011=0.25×14.5 million=3.625 million ext{Households in 2011} = 0.25 \times 14.5 \text{ million} = 3.625 \text{ million}

Calculating the decrease:

extDecrease=3.625 million−3.564 million=0.061 million ext{Decrease} = 3.625 \text{ million} - 3.564 \text{ million} = 0.061 \text{ million}

Since the statement indicates a decrease of 0.060 million, the verification implies the statement is incorrect because the actual decrease is 0.061 million.

Step 5

Explain why the percentages for the 1996 census do not add up to 100%.

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Answer

The percentages for the 1996 census do not add up to 100% because there are likely households with sizes not explicitly listed, or due to rounding in the reported data.

Step 6

Write down the probability of randomly choosing a household from the 2011 census with a household size fewer than four persons.

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Answer

To find the probability of randomly choosing a household with fewer than four persons from the 2011 census:

The percentage of households with fewer than four persons is:

  • Households with 1 person: 27%
  • Households with 2 persons: 18%
  • Households with 3 persons: 11%

Total = 27% + 18% + 11% = 56%.

Therefore, the probability is:

P=0.56extor56%.P = 0.56 ext{ or } 56\%.

Step 7

Write down the modal class for the income per capita per day.

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Answer

The modal class for the income per capita per day is 'R280 and more' as it has the highest percentage of households at 11%.

Step 8

Determine the total number of households with a per capita income of less than R80 per day.

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Answer

To find the total number of households with a per capita income of less than R80:

  • Households with less than R20: 3.2 million
  • Households with R20 to R79: 3.1 million

Total = 3.2 million + 3.1 million = 6.3 million households.

Step 9

Calculate the Wong household income per capita per day.

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Answer

The total annual income of the Wong family is:

extTotalincome=R276,000+R541,500=R817,500 ext{Total income} = R276,000 + R541,500 = R817,500

The household size is:

extHouseholdsize=1+1+0.5+0.5=3ext(2children,eachcountsas0.5) ext{Household size} = 1 + 1 + 0.5 + 0.5 = 3 ext{ (2 children, each counts as 0.5)}

Thus, the per capita income per day is:

extPercapitaincome=R817,5003×365≈R749.32extperday ext{Per capita income} = \frac{R817,500}{3 \times 365} \approx R749.32 ext{ per day}

Step 10

Determine the total amount spent by this household on cellphones per year.

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Answer

To find the total amount spent on cellphones:

The income per capita per day is R280. Spending on cellphones is 4%:

extAmountspentperday=0.04×R280=R11.20extperday ext{Amount spent per day} = 0.04 \times R280 = R11.20 ext{ per day}

Now, calculating the annual expenditure:

extTotalspentperyear=R11.20×365=R4,088extperyear ext{Total spent per year} = R11.20 \times 365 = R4,088 ext{ per year}

Step 11

Calculate, in millions, the total that was spent by all the households on electricity and tap water in 2011.

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Answer

The average expenditure on electricity and tap water:

Electricity: 12.1 million households Average expenditure = R125 Total on electricity:

extTotalspentonelectricity=12.1extmillion×R125×12=R15,187.5extmillion ext{Total spent on electricity} = 12.1 ext{ million} \times R125 \times 12 = R15,187.5 ext{ million}

Water: 12.1 million households Average expenditure = R98 Total on water:

extTotalspentonwater=12.1extmillion×R98×12=R14,242.4extmillion ext{Total spent on water} = 12.1 ext{ million} \times R98 \times 12 = R14,242.4 ext{ million}

Thus, the total spent on both:

extTotalspent=R15,187.5+R14,242.4=R29,429.9extmillion ext{Total spent} = R15,187.5 + R14,242.4 = R29,429.9 ext{ million}

Step 12

Give ONE reason for the difference in the length of the bars for each of the graphs.

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Answer

One reason for the difference in the length of the bars for each of the graphs could be the changes in the total number of households or variations in service provision across the years.

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