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Answer :
Alright, let's break down the solution for each part of the question step-by-step.
### 1.1.7 Determine the median of Task 1's marks.
The median is the middle value when the numbers are sorted in ascending order. If there's an even number of observations, the median is the average of the two middle numbers.
Given marks:
[tex]\[ 24, 14, 16, 6, 8, 14, 20, 26, 2, 24, 14, 20, 4, 2, 22, 24, 28, 8, 29, 4, 22, 14, 14, 16, 8, 14, 22, 18, 20, 30 \][/tex]
Step-by-step:
1. Sort the marks:
[tex]\[ 2, 2, 4, 4, 6, 8, 8, 8, 14, 14, 14, 14, 14, 14, 16, 16, 18, 20, 20, 20, 22, 22, 22, 24, 24, 24, 26, 28, 29, 30 \][/tex]
2. Find the middle value(s):
- There are 30 marks (even number), so the median is the average of the 15th and 16th marks.
- The 15th and 16th marks are both 16.
Median:
[tex]\[ \text{Median} = 16 \][/tex]
### 1.2.1 Complete the tally and frequency table
Marks and their frequencies are found as follows:
[tex]\[ \begin{array}{|c|c|}
\hline
\text{Marks} & \text{Frequency} \\
\hline
2 & 2 \\
4 & 2 \\
6 & 1 \\
8 & 3 \\
14 & 6 \\
16 & 2 \\
18 & 1 \\
20 & 3 \\
22 & 3 \\
24 & 3 \\
26 & 1 \\
28 & 1 \\
29 & 1 \\
30 & 1 \\
\hline
\end{array} \][/tex]
### 1.2.2 Determine the mode of the test marks
The mode is the number that appears most frequently in the list.
- The frequency table shows that 14 appears 6 times, which is the highest frequency.
Mode:
[tex]\[ \text{Mode} = 14 \][/tex]
### 1.2.3 Determine the range of the test marks
The range is the difference between the highest and lowest values.
- Highest mark: 30
- Lowest mark: 2
Range:
[tex]\[ \text{Range} = 30 - 2 = 28 \][/tex]
### 1.2.4 Calculate the mean mark
The mean is the average of all the marks.
1. Sum of marks:
[tex]\[ 24 + 14 + 16 + 6 + 8 + 14 + 20 + 26 + 2 + 24 + 14 + 20 + 4 + 2 + 22 + 24 + 28 + 8 + 29 + 4 + 22 + 14 + 14 + 16 + 8 + 14 + 22 + 18 + 20 + 30 = 476 \][/tex]
2. Number of marks: 30
Mean:
[tex]\[ \text{Mean} = \frac{476}{30} \approx 16 \][/tex]
### 1.2.5 If the pass mark is 12, how many students passed the test?
Count the number of students with marks ≥ 12:
[tex]\[ 24, 14, 16, 14, 20, 26, 24, 14, 20, 22, 24, 28, 29, 22, 14, 14, 16, 14, 22, 18, 20, 30 \][/tex]
- There are 22 such marks.
Number of students who passed:
[tex]\[ 22 \][/tex]
### 1.2.6 What percentage of the students achieved 50% or more?
The test is out of 40 marks, so 50% is 20 marks.
Count the number of students with marks ≥ 20:
[tex]\[ 24, 20, 26, 24, 20, 22, 24, 28, 29, 22, 22, 20, 30 \][/tex]
- There are 13 such marks.
Total number of students: 30
Percentage:
[tex]\[ \text{Percentage} = \left(\frac{13}{30} \times 100\right) \approx 43.33\% \][/tex]
### 1.2.7 Draw and label a histogram
To draw the histogram:
1. Mark the horizontal axis with the score ranges (e.g., 0-5, 6-10, 11-15, etc.)
2. Mark the vertical axis with frequencies.
3. For each score range, draw a bar up to the corresponding frequency from the frequency table.
Note: The histogram creation cannot be shown textually here, but the steps give a clear guide on how to draw it using the grid provided in Addendum A.
In summary, the results are:
- Median: 16
- Mode: 14
- Range: 28
- Mean: 16
- Number of students who passed: 22
- Percentage of students with 50% or more: 43.33%
Feel free to ask if you have any more questions!
### 1.1.7 Determine the median of Task 1's marks.
The median is the middle value when the numbers are sorted in ascending order. If there's an even number of observations, the median is the average of the two middle numbers.
Given marks:
[tex]\[ 24, 14, 16, 6, 8, 14, 20, 26, 2, 24, 14, 20, 4, 2, 22, 24, 28, 8, 29, 4, 22, 14, 14, 16, 8, 14, 22, 18, 20, 30 \][/tex]
Step-by-step:
1. Sort the marks:
[tex]\[ 2, 2, 4, 4, 6, 8, 8, 8, 14, 14, 14, 14, 14, 14, 16, 16, 18, 20, 20, 20, 22, 22, 22, 24, 24, 24, 26, 28, 29, 30 \][/tex]
2. Find the middle value(s):
- There are 30 marks (even number), so the median is the average of the 15th and 16th marks.
- The 15th and 16th marks are both 16.
Median:
[tex]\[ \text{Median} = 16 \][/tex]
### 1.2.1 Complete the tally and frequency table
Marks and their frequencies are found as follows:
[tex]\[ \begin{array}{|c|c|}
\hline
\text{Marks} & \text{Frequency} \\
\hline
2 & 2 \\
4 & 2 \\
6 & 1 \\
8 & 3 \\
14 & 6 \\
16 & 2 \\
18 & 1 \\
20 & 3 \\
22 & 3 \\
24 & 3 \\
26 & 1 \\
28 & 1 \\
29 & 1 \\
30 & 1 \\
\hline
\end{array} \][/tex]
### 1.2.2 Determine the mode of the test marks
The mode is the number that appears most frequently in the list.
- The frequency table shows that 14 appears 6 times, which is the highest frequency.
Mode:
[tex]\[ \text{Mode} = 14 \][/tex]
### 1.2.3 Determine the range of the test marks
The range is the difference between the highest and lowest values.
- Highest mark: 30
- Lowest mark: 2
Range:
[tex]\[ \text{Range} = 30 - 2 = 28 \][/tex]
### 1.2.4 Calculate the mean mark
The mean is the average of all the marks.
1. Sum of marks:
[tex]\[ 24 + 14 + 16 + 6 + 8 + 14 + 20 + 26 + 2 + 24 + 14 + 20 + 4 + 2 + 22 + 24 + 28 + 8 + 29 + 4 + 22 + 14 + 14 + 16 + 8 + 14 + 22 + 18 + 20 + 30 = 476 \][/tex]
2. Number of marks: 30
Mean:
[tex]\[ \text{Mean} = \frac{476}{30} \approx 16 \][/tex]
### 1.2.5 If the pass mark is 12, how many students passed the test?
Count the number of students with marks ≥ 12:
[tex]\[ 24, 14, 16, 14, 20, 26, 24, 14, 20, 22, 24, 28, 29, 22, 14, 14, 16, 14, 22, 18, 20, 30 \][/tex]
- There are 22 such marks.
Number of students who passed:
[tex]\[ 22 \][/tex]
### 1.2.6 What percentage of the students achieved 50% or more?
The test is out of 40 marks, so 50% is 20 marks.
Count the number of students with marks ≥ 20:
[tex]\[ 24, 20, 26, 24, 20, 22, 24, 28, 29, 22, 22, 20, 30 \][/tex]
- There are 13 such marks.
Total number of students: 30
Percentage:
[tex]\[ \text{Percentage} = \left(\frac{13}{30} \times 100\right) \approx 43.33\% \][/tex]
### 1.2.7 Draw and label a histogram
To draw the histogram:
1. Mark the horizontal axis with the score ranges (e.g., 0-5, 6-10, 11-15, etc.)
2. Mark the vertical axis with frequencies.
3. For each score range, draw a bar up to the corresponding frequency from the frequency table.
Note: The histogram creation cannot be shown textually here, but the steps give a clear guide on how to draw it using the grid provided in Addendum A.
In summary, the results are:
- Median: 16
- Mode: 14
- Range: 28
- Mean: 16
- Number of students who passed: 22
- Percentage of students with 50% or more: 43.33%
Feel free to ask if you have any more questions!
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