Answer :
### 2.1.1 Draw a stem and leaf plot showing the marks of the students
A stem-and-leaf plot is a way to display data where each number is split into two parts:
- The "stem" is the leading digit(s)
- The "leaf" is the trailing digit.
Given the marks:
[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline 55 & 56 & 70 & 60 & 60 \\ \hline 56 & 70 & 60 & 54 & 60 \\ \hline 58 & 51 & 52 & 46 & 84 \\ \hline 47 & 72 & 82 & 48 & 81 \\ \hline 69 & 77 & 53 & 48 & 82 \\ \hline \end{tabular} \][/tex]
We organize the data into stems (tens place) and leaves (ones place):
[tex]\[ \begin{tabular}{cc} Stem & Leaf \\ \hline 4 & 6, 7, 8, 8 \\ 5 & 1, 2, 3, 4, 5, 6, 6, 8 \\ 6 & 0, 0, 0, 0, 9 \\ 7 & 0, 0, 2, 7 \\ 8 & 1, 2, 2, 4 \\ \end{tabular} \][/tex]
### 2.1.2 Calculate the mean percentage marks for the students
The mean (average) percentage is calculated by summing all the marks and then dividing by the number of students.
Mean percentage = [tex]\( \frac{\text{Sum of all marks}}{\text{Number of students}} \)[/tex]
[tex]\[ \text{Sum of marks} = 55 + 56 + 70 + 60 + 60 + 56 + 70 + 60 + 54 + 60 + 58 + 51 + 52 + 46 + 84 + 47 + 72 + 82 + 48 + 81 + 69 + 77 + 53 + 48 + 82 = 1551 \][/tex]
[tex]\[ \text{Number of students} = 25 \][/tex]
[tex]\[ \text{Mean percentage} = \frac{1551}{25} = 62.04 \][/tex]
### 2.1.3 Calculate the median percentage marks for the students
The median is the middle number in a sorted list. If the number of data points is odd, the median is the middle number. If the number of data points is even, it is the average of the two middle numbers.
First, let's sort the marks:
[tex]\[ 46, 47, 48, 48, 51, 52, 53, 54, 55, 56, 56, 58, 60, 60, 60, 60, 69, 70, 70, 72, 77, 81, 82, 82, 84 \][/tex]
Since there are 25 students (an odd number), the median is the 13th number in the sorted list:
[tex]\[ \text{Median percentage} = 60.0 \][/tex]
### 2.1.4 Calculate the range percentage marks for the students
The range is the difference between the highest and lowest values in the dataset.
[tex]\[ \text{Lowest mark} = 46 \][/tex]
[tex]\[ \text{Highest mark} = 84 \][/tex]
[tex]\[ \text{Range percentage} = 84 - 46 = 38 \][/tex]
### 2.1.5 Write down the mode of percentage marks for the students
The mode is the number that appears most frequently in the dataset.
From the given marks, we see that the mark 60 appears most frequently (4 times):
[tex]\[ \text{Mode percentage} = 60 \][/tex]
### Summary
1. Stem and Leaf Plot:
[tex]\[ \begin{tabular}{cc} Stem & Leaf \\ \hline 4 & 6, 7, 8, 8 \\ 5 & 1, 2, 3, 4, 5, 6, 6, 8 \\ 6 & 0, 0, 0, 0, 9 \\ 7 & 0, 0, 2, 7 \\ 8 & 1, 2, 2, 4 \\ \end{tabular} \][/tex]
2. Mean Percentage: 62.04
3. Median Percentage: 60.0
4. Range Percentage: 38
5. Mode Percentage: 60
A stem-and-leaf plot is a way to display data where each number is split into two parts:
- The "stem" is the leading digit(s)
- The "leaf" is the trailing digit.
Given the marks:
[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline 55 & 56 & 70 & 60 & 60 \\ \hline 56 & 70 & 60 & 54 & 60 \\ \hline 58 & 51 & 52 & 46 & 84 \\ \hline 47 & 72 & 82 & 48 & 81 \\ \hline 69 & 77 & 53 & 48 & 82 \\ \hline \end{tabular} \][/tex]
We organize the data into stems (tens place) and leaves (ones place):
[tex]\[ \begin{tabular}{cc} Stem & Leaf \\ \hline 4 & 6, 7, 8, 8 \\ 5 & 1, 2, 3, 4, 5, 6, 6, 8 \\ 6 & 0, 0, 0, 0, 9 \\ 7 & 0, 0, 2, 7 \\ 8 & 1, 2, 2, 4 \\ \end{tabular} \][/tex]
### 2.1.2 Calculate the mean percentage marks for the students
The mean (average) percentage is calculated by summing all the marks and then dividing by the number of students.
Mean percentage = [tex]\( \frac{\text{Sum of all marks}}{\text{Number of students}} \)[/tex]
[tex]\[ \text{Sum of marks} = 55 + 56 + 70 + 60 + 60 + 56 + 70 + 60 + 54 + 60 + 58 + 51 + 52 + 46 + 84 + 47 + 72 + 82 + 48 + 81 + 69 + 77 + 53 + 48 + 82 = 1551 \][/tex]
[tex]\[ \text{Number of students} = 25 \][/tex]
[tex]\[ \text{Mean percentage} = \frac{1551}{25} = 62.04 \][/tex]
### 2.1.3 Calculate the median percentage marks for the students
The median is the middle number in a sorted list. If the number of data points is odd, the median is the middle number. If the number of data points is even, it is the average of the two middle numbers.
First, let's sort the marks:
[tex]\[ 46, 47, 48, 48, 51, 52, 53, 54, 55, 56, 56, 58, 60, 60, 60, 60, 69, 70, 70, 72, 77, 81, 82, 82, 84 \][/tex]
Since there are 25 students (an odd number), the median is the 13th number in the sorted list:
[tex]\[ \text{Median percentage} = 60.0 \][/tex]
### 2.1.4 Calculate the range percentage marks for the students
The range is the difference between the highest and lowest values in the dataset.
[tex]\[ \text{Lowest mark} = 46 \][/tex]
[tex]\[ \text{Highest mark} = 84 \][/tex]
[tex]\[ \text{Range percentage} = 84 - 46 = 38 \][/tex]
### 2.1.5 Write down the mode of percentage marks for the students
The mode is the number that appears most frequently in the dataset.
From the given marks, we see that the mark 60 appears most frequently (4 times):
[tex]\[ \text{Mode percentage} = 60 \][/tex]
### Summary
1. Stem and Leaf Plot:
[tex]\[ \begin{tabular}{cc} Stem & Leaf \\ \hline 4 & 6, 7, 8, 8 \\ 5 & 1, 2, 3, 4, 5, 6, 6, 8 \\ 6 & 0, 0, 0, 0, 9 \\ 7 & 0, 0, 2, 7 \\ 8 & 1, 2, 2, 4 \\ \end{tabular} \][/tex]
2. Mean Percentage: 62.04
3. Median Percentage: 60.0
4. Range Percentage: 38
5. Mode Percentage: 60
