Certainly! Let's determine the required values step by step.
### a) Work out the range of the marks.
The range of a set of data is the difference between the highest and lowest values. From the given marks:
Marks: 6, 7, 8, 9, 10
- The highest mark is 10.
- The lowest mark is 6.
Range = Highest mark - Lowest mark = 10 - 6 = 4.
Range of the marks = 4
### b) How many students are in the group?
The total number of students can be found by summing the frequencies of all the marks.
Frequencies: 5, 4, 7, 10, 4
Total number of students = 5 + 4 + 7 + 10 + 4 = 30.
Total number of students in the group = 30
### c) Work out the mean mark of the group.
The mean (average) mark is calculated by dividing the total sum of the marks by the total number of students.
First, calculate the total sum of the marks:
- Marks: 6, 7, 8, 9, 10
- Frequencies: 5, 4, 7, 10, 4
Total sum of marks = (6 5) + (7 4) + (8 7) + (9 10) + (10 * 4)
= 30 + 28 + 56 + 90 + 40
= 244.
Now, divide the total sum of marks by the total number of students to find the mean:
- Total sum of marks = 244
- Total number of students = 30
Mean mark = Total sum of marks / Total number of students
= 244 / 30
≈ 8.1333 (to 4 decimal places).
Mean mark of the group ≈ 8.1333
Thus, the detailed solution steps are:
- Range of the marks: 4
- Total number of students: 30
- Mean mark of the group: 8.1333
