Election Data Analysis: Centre S Invalid Vote Percentage

This question involves calculating the percentage of invalid votes cast at Centre S relative to the total number of registered voters. We need to first determine the number of votes cast at Centre S, then find the number of invalid votes, and finally express this as a percentage of the registered voters.

Step 1: Presenting the Data for Centre S

The table provided contains the following information relevant to Centre S:

From the table, we know:

• Total Registered Voters at Centre S = 1850
• Percentage of Voters who Voted at Centre S = 90%

Calculating Total Votes Cast at Centre S

To find the total number of votes cast, we calculate 90% of the registered voters at Centre S:

Number of Votes Cast = Total Registered Voters × Percentage Voted

Number of Votes Cast = $1850 \times \frac{90}{100}$

Number of Votes Cast = $1850 \times 0.90$

Number of Votes Cast = $1665$

So, 1665 people cast their votes at Centre S.

Calculating the Number of Invalid Votes at Centre S

The question states that the number of invalid votes was 20% of the total number of votes cast.

Number of Invalid Votes = Total Votes Cast × Percentage of Invalid Votes

Number of Invalid Votes = $1665 \times \frac{20}{100}$

Number of Invalid Votes = $1665 \times 0.20$

Number of Invalid Votes = $333$

Therefore, there were 333 invalid votes at Centre S.

Determining Percentage of Registered Voters with Invalid Votes

The final step is to find what percentage these 333 invalid votes represent out of the total number of registered voters (1850).

Percentage of Registered Voters (Invalid Votes) = $ \frac{\text{Number of Invalid Votes}}{\text{Total Registered Voters}} \times 100 $

Percentage = $ \frac{333}{1850} \times 100 $

Percentage = $ 0.18 \times 100 $

Percentage = $ 18\% $

Thus, 18% of the total number of registered voters at Centre S cast invalid votes.