Certainly! Let's work through each part of the question step-by-step, using the provided table of marks and their frequencies.
### a) Work out the range of the marks.
The range is the difference between the highest and the lowest marks.
From the table:
- The lowest mark is 6.
- The highest mark is 10.
Range = Highest mark - Lowest mark
Range = 10 - 6
Therefore, the range of the marks is 4.
### b) How many students are in the group?
To find the total number of students, we sum the frequencies of all the marks.
From the table:
- Number of students with a mark of 6: 5
- Number of students with a mark of 7: 4
- Number of students with a mark of 8: 7
- Number of students with a mark of 9: 10
- Number of students with a mark of 10: 4
Total number of students = 5 + 4 + 7 + 10 + 4
Total number of students = 30
Therefore, there are 30 students in the group.
### c) Work out the mean mark of the group
The mean mark is calculated by dividing the total sum of all marks by the total number of students.
First, we find the total sum of all marks:
- Total sum of marks = (Mark 6 Frequency 5) + (Mark 7 Frequency 4) + (Mark 8 Frequency 7) + (Mark 9 Frequency 10) + (Mark 10 Frequency 4)
- Total sum of marks = (6 5) + (7 4) + (8 7) + (9 10) + (10 4)
- Total sum of marks = 30 + 28 + 56 + 90 + 40
Total sum of marks = 244
Next, we calculate the mean mark:
Mean mark = Total sum of marks / Total number of students
Mean mark = 244 / 30
Mean mark ≈ 8.13
Therefore, the mean mark of the group is approximately 8.13.
To summarize:
a) The range of the marks is 4.
b) The total number of students in the group is 30.
c) The mean mark of the group is approximately 8.13.
