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QUESTION 1: UNDERSTANDING THE DATA Refer to pages 2 and 3: Based on the option you selected, answer the following questions: The table below shows the number of reported incidents of burglary and fire cases in South Africa over five years.

Mathematics

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Answers

4 parts
1.1

2021\text{2021}

1.2

2024\text{2024}

1.3
931
2.1
1391.6

Step-by-step solution

9 steps

Based on your notes, you have selected "Number of Burglaries" (Option 1) for your calculations.

Here is the data for the number of burglaries:

  • 2020: 1145
  • 2021: 1981
  • 2022: 1203
  • 2023: 1579
  • 2024: 1050

Part 1.1· 2 steps

In which year was the number of burglary/fire incidents the highest?

  1. Identify the highest number of burglaries from the given data.

    The numbers are $1145, 1981, 1203, 1579, 1050$.
    The highest value is 1981.

  2. Determine the year corresponding to the highest value.

    The year corresponding to 1981 burglaries is 2021.
    The student's note "deet Burglary = 2021" is correct.

    The year with the highest number of burglary incidents was 2021\boxed{\text{2021}}.

Part 1.2

2024\text{2024}

In which year was the number of burglary/fire incidents the lowest?

  1. Identify the lowest number of burglaries from the given data.

    The numbers are $1145, 1981, 1203, 1579, 1050$.
    The lowest value is 1050.

  2. Determine the year corresponding to the lowest value.

    The year corresponding to 1050 burglaries is 2024.

    The year with the lowest number of burglary incidents was 2024\boxed{\text{2024}}.

Part 1.3931

Calculate the range of burglary/fire incidents.

  1. Identify the highest and lowest number of burglary incidents.

    Highest number of burglaries =1981= 1981
    Lowest number of burglaries =1050= 1050

  2. Calculate the range using the formula

    Range = Highest value - Lowest value.

    Range=1981−1050\text{Range} = 1981 - 1050 Range=931\text{Range} = 931

    The range of burglary incidents is 931\boxed{931}.

Part 2.11391.6

Calculate the mean of burglary/fire incidents over the five years.

  1. Sum all the burglary incidents over the five years.

    Sum=1145+1981+1203+1579+1050\text{Sum} = 1145 + 1981 + 1203 + 1579 + 1050 Sum=6958\text{Sum} = 6958
  2. Count the number of years.

    There are 5 years ($2020, 2021, 2022, 2023, 2024$).

  3. Calculate the mean using the formula

    Mean = Sum of valuesNumber of values\frac{\text{Sum of values}}{\text{Number of values}}.

    Mean=69585\text{Mean} = \frac{6958}{5} Mean=1391.6\text{Mean} = 1391.6

    The mean number of burglary incidents over the five years is 1391.6\boxed{1391.6}.

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