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Worksheet 1B - MATHEMATICS [FORMAL ASSESSMENT] 2.2 Determine the median of burglary/fire incidents over the five years. 2.3 Explain what the mean tells us about incidents of burglary/fire trends in South Africa over the five years.

Mathematics

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2 parts
2.2
1203
3.1

33.50%33.50\%

1145

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Here are the solutions for the next set of questions:

Part 2.2· 2 steps

Determine the median of burglary/fire incidents over the five years.

  1. List the number of burglary incidents for each year in ascending order.

    The incidents are: $1145, 1981, 1203, 1579, 1050$.
    Sorted list: $1050, 1145, 1203, 1579, 1981$.

  2. Find the median.

    Since there are 5 data points (an odd number), the median is the middle value.
    The middle value is the 3rd3^{\text{rd}} term in the sorted list.
    The 3rd3^{\text{rd}} term is 1203.

    The median number of burglary incidents is 1203\boxed{1203}.

Part 2.3

Explain what the mean tells us about incidents of burglary/fire trends in South Africa over the five years.

The mean of 1391.6 represents the average number of burglary/fire incidents per year over the five-year period. It provides a central value that summarizes the typical level of incidents, allowing for a general understanding of the trend without focusing on individual year fluctuations.

Part 3

PERCENTAGE INCREASE AND DECREASE

Part 3.1

33.50%33.50\%

Calculate the percentage decrease in burglary/fire incidents from 2023 to 2024.

  1. Identify the number of incidents in 2023 and 2024.

    Incidents in 2023=15792023 = 1579
    Incidents in 2024=10502024 = 1050

  2. Calculate the decrease in incidents.

    Decrease=1579−1050=529\text{Decrease} = 1579 - 1050 = 529
  3. Calculate the percentage decrease using the formula

    DecreaseOriginal Value×100%\frac{\text{Decrease}}{\text{Original Value}} \times 100\%.

    Percentage Decrease=5291579×100%\text{Percentage Decrease} = \frac{529}{1579} \times 100\% Percentage Decrease≈33.50%\text{Percentage Decrease} \approx 33.50\%

    The percentage decrease in burglary/fire incidents from 2023 to 2024 is 33.50%\boxed{33.50\%}.

    3.2 The number of reported burglary or fire incidents increased by an average of 9% from 2024 to 2025. Using the number of incidents recorded in 2024, calculate and predict the number of incidents for 2025.

  4. Identify the number of incidents in 2024.

    Incidents in 2024=10502024 = 1050

  5. Calculate the 9%9\% increase.

    Increase amount=0.09×1050\text{Increase amount} = 0.09 \times 1050 Increase amount=94.5\text{Increase amount} = 94.5
  6. Add the increase to the 2024 incidents to predict the 2025 incidents.

    Incidents in 2025=1050+94.5\text{Incidents in 2025} = 1050 + 94.5 Incidents in 2025=1144.5\text{Incidents in 2025} = 1144.5

    Since the number of incidents must be a whole number, we round to the nearest whole number.

    Incidents in 2025≈1145\text{Incidents in 2025} \approx 1145

    The predicted number of incidents for 2025 is 1145\boxed{1145}.

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