Sure, let's break down the steps to answer each part of the question based on the given data:
\begin{tabular}{|c|c|}
\hline
Mark & Frequency \\
\hline
6 & 2 \\
\hline
7 & 4 \\
\hline
8 & 7 \\
\hline
9 & 8 \\
\hline
10 & 3 \\
\hline
\end{tabular}
### a) Work out the range of the marks.
The range is the difference between the highest and lowest marks.
- The highest mark in the table is [tex]\(10\)[/tex].
- The lowest mark in the table is [tex]\(6\)[/tex].
So, the range is:
[tex]\[ \text{Range} = 10 - 6 = 4 \][/tex]
### b) How many students are in the group?
To find out how many students are in the group, we sum up the frequencies.
[tex]\[
2 + 4 + 7 + 8 + 3 = 24
\][/tex]
So, the total number of students in the group is [tex]\(24\)[/tex].
### c) Work out the mean mark of the group.
To calculate the mean mark, we need to follow these steps:
1. Multiply each mark by its frequency to get the total marks for each score range.
2. Sum these total marks.
3. Divide this sum by the total number of students.
Total marks = [tex]\( (6 \times 2) + (7 \times 4) + (8 \times 7) + (9 \times 8) + (10 \times 3) \)[/tex]
Calculate each term:
[tex]\[
6 \times 2 = 12
\][/tex]
[tex]\[
7 \times 4 = 28
\][/tex]
[tex]\[
8 \times 7 = 56
\][/tex]
[tex]\[
9 \times 8 = 72
\][/tex]
[tex]\[
10 \times 3 = 30
\][/tex]
Sum these values:
[tex]\[
12 + 28 + 56 + 72 + 30 = 198
\][/tex]
Now, divide this sum by the total number of students:
[tex]\[
\text{Mean mark} = \frac{198}{24} = 8.25
\][/tex]
### Final Answers:
a) The range of the marks is [tex]\(4\)[/tex].
b) The total number of students in the group is [tex]\(24\)[/tex].
c) The mean mark of the group is [tex]\(8.25\)[/tex].
