Sure, let's solve the given problem step-by-step.
### 2.1.1. Calculate the mean mark of both colleges
To find the mean mark of the students from each college, we sum all their marks and then divide by the number of students.
College 1:
[tex]\[ \text{Marks} = [55, 45, 65, 85, 25, 45, 50, 89, 96] \][/tex]
[tex]\[ \text{Number of students} = 9 \][/tex]
[tex]\[ \text{Mean} = \frac{55 + 45 + 65 + 85 + 25 + 45 + 50 + 89 + 96}{9} \][/tex]
[tex]\[ \text{Mean} = \frac{555}{9} \approx 61.67 \][/tex]
College 2:
[tex]\[ \text{Marks} = [75, 58, 69, 80, 46, 87, 89, 53, 49] \][/tex]
[tex]\[ \text{Number of students} = 9 \][/tex]
[tex]\[ \text{Mean} = \frac{75 + 58 + 69 + 80 + 46 + 87 + 89 + 53 + 49}{9} \][/tex]
[tex]\[ \text{Mean} = \frac{606}{9} = 67.33 \][/tex]
So, the mean mark of College 1 is approximately [tex]\( 61.67\%\)[/tex] and the mean mark of College 2 is [tex]\( 67.33\%\)[/tex].
### 2.1.2. What is the range of both colleges?
The range of a set of numbers is the difference between the maximum and minimum values in the set.
College 1:
[tex]\[ \text{Marks} = [55, 45, 65, 85, 25, 45, 50, 89, 96] \][/tex]
[tex]\[ \text{Max value} = 96 \][/tex]
[tex]\[ \text{Min value} = 25 \][/tex]
[tex]\[ \text{Range} = 96 - 25 = 71 \][/tex]
College 2:
[tex]\[ \text{Marks} = [75, 58, 69, 80, 46, 87, 89, 53, 49] \][/tex]
[tex]\[ \text{Max value} = 89 \][/tex]
[tex]\[ \text{Min value} = 46 \][/tex]
[tex]\[ \text{Range} = 89 - 46 = 43 \][/tex]
So, the range of College 1 is 71 and the range of College 2 is 43.
### 2.1.3. Calculate the median mark of College 1
To find the median, we need to arrange the marks in ascending order and then find the middle value. If there is an even number of values, we take the average of the two middle numbers.
College 1:
[tex]\[ \text{Marks} = [55, 45, 65, 85, 25, 45, 50, 89, 96] \][/tex]
[tex]\[ \text{Sorted marks} = [25, 45, 45, 50, 55, 65, 85, 89, 96] \][/tex]
There are 9 values, so the median is the 5th value in the sorted list.
[tex]\[ \text{Median} = 55 \][/tex]
So, the median mark of College 1 is [tex]\( 55\%\)[/tex].
### 2.1.4. Find the mode of the College 1
The mode is the value that appears most frequently in the data set.
College 1:
[tex]\[ \text{Marks} = [55, 45, 65, 85, 25, 45, 50, 89, 96] \][/tex]
The value 45 appears twice, which is more frequent than any other value in this list.
So, the mode of College 1 marks is [tex]\( 45\%\)[/tex].
