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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 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}} imes 100

Here, the total number of households in 1996 was 8.7 million and in 2011 was 14.5 million.

Calculating:

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

(a) This indicates that the total number of households has increased significantly over the years.

(b) The data does not suggest a constant number, as the increase is substantial.

Step 2

4.1.3 Verify the statement regarding the number of households with five or more persons.

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Answer

To verify the statement regarding households with five or more persons:

From the census:

  • In 2001, the percentage was 33% out of 10.8 million households:
extNumberofhouseholds=0.33imes10.8extmillion=3.564extmillion ext{Number of households} = 0.33 imes 10.8 ext{ million} = 3.564 ext{ million}
  • In 2011, the percentage was 25% out of 14.5 million households:
extNumberofhouseholds=0.25imes14.5extmillion=3.625extmillion ext{Number of households} = 0.25 imes 14.5 ext{ million} = 3.625 ext{ million}

The decrease is:

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

The statement is incorrect since the decrease is 0.061 million, not 0.060 million.

Step 3

4.1.4 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% due to rounding. When percentages are rounded to whole numbers, small discrepancies can occur in the total, leading to the sum being less than 100%. Additionally, the last category 'Five or more' may include other variable household sizes that don't capture all instances.

Step 4

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 the probability of randomly selecting a household with fewer than four persons from the 2011 census:

The percentages for households with sizes fewer than four are:

  • One person: 27%
  • Two persons: 19%
  • Three persons: 11%

Calculating the total percentage:

ext{Total Percentage} = 27 ext{%} + 19 ext{%} + 11 ext{%} = 57 ext{%}

Thus, the probability of randomly choosing a household with fewer than four persons is:

P( ext{fewer than 4}) = 0.57 ext{ or } 57 ext{%}

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