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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

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

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Answer

To calculate the percentage increase, use the formula:

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

Here, the old value (1996) is 8.7 million and the new value (2011) is 14.5 million:

ext{Percentage Increase} = rac{14.5 - 8.7}{8.7} imes 100 = rac{5.8}{8.7} imes 100 \\ ext{Percentage Increase} \\ ext{≈} 66.67\%

Step 2

4.1.2 (a) Increased every year, but only by a small percentage.

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Answer

This statement is true as the total number of households increased from 8.7 million (1996) to 10.8 million (2001) and then to 14.5 million (2011), reflecting an increase each year.

Step 3

4.1.2 (b) Remained constant in every census from 1996 to 2011.

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Answer

This statement is false as the numbers clearly show an increase in the number of households in each census.

Step 4

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

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Answer

To verify the decrease in the number of households with five or more persons between 2001 and 2011:

From the data:

  • 2001: 33% of 10.8 million = 3.564 million
  • 2011: 25% of 14.5 million = 3.625 million

Now, calculating the difference:

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

This indicates an increase rather than a decrease. Therefore, the statement is INCORRECT.

Step 5

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

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Answer

The percentages do not add up to 100% because they represent only the percentage of households within specific groupings. Other households could fall into categories not represented in the provided data, leading to a total less than 100%.

Step 6

4.1.5 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 this probability, calculate the percentage of households with fewer than four persons:

  • One: 27%
  • Two: 20%
  • Three: 11%

Total: 27 + 20 + 11 = 58%

The probability is:

P(extfewerthan4persons)=0.58extor58%P( ext{fewer than 4 persons}) = 0.58 ext{ or } 58\%

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