Sure, let's solve the questions step by step.
### a) Work out the range of the marks
The range of a set of values is the difference between the highest value and the lowest value. Here, the marks range from the minimum value of 6 to the maximum value of 10.
So, the range of the marks is:
[tex]\[ \text{Range} = \text{Maximum mark} - \text{Minimum mark} = 10 - 6 = 4 \][/tex]
### b) How many students are in the group?
The total number of students can be found by summing the frequencies of all the marks. The frequencies given are:
- 5 students scored 6,
- 4 students scored 7,
- 7 students scored 8,
- 10 students scored 9,
- 4 students scored 10.
Adding these together, the total number of students is:
[tex]\[ 5 + 4 + 7 + 10 + 4 = 30 \][/tex]
So, 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 the marks by the total number of students. First, we calculate the total sum of all the marks, considering their frequencies:
[tex]\[ (6 \times 5) + (7 \times 4) + (8 \times 7) + (9 \times 10) + (10 \times 4) = 30 + 28 + 56 + 90 + 40 = 244 \][/tex]
Now, we divide this total by the number of students to find the mean:
[tex]\[ \text{Mean mark} = \frac{\text{Total sum of marks}}{\text{Total number of students}} = \frac{244}{30} \approx 8.13333 \][/tex]
So, the mean mark of the group is approximately 8.13.
### Summary of the Results
- The range of the marks is 4.
- The total number of students is 30.
- The mean mark is approximately 8.13.
