Consider the following set of marks for a class test (out of 10) for grade 8 A. Rearrange these marks in an ascending order, write down the mode, determine the median, calculate the mean, and calculate the range for this set.

The marks are $8, 6, 4, 10, 5, 8, 8, 6$.

The marks in ascending order are: $\boxed{\text{4, 5, 6, 6, 8, 8, 8, 10}}$

1.1.2 Write down the mode of this set of marks

The sorted marks are $4, 5, 6, 6, 8, 8, 8, 10$.

• 4 appears once.
• 5 appears once.
• 6 appears twice.
• 8 appears three times.
• 10 appears once.

The mark that appears most often is 8.
The mode is: $\boxed{8}$

1.1.3 Determine the median for this set

The sorted marks are $4, 5, 6, 6, 8, 8, 8, 10$.
There are $n=8$ marks, which is an even number.

For an even number of data points, the median is the average of the $\left(\frac{n}{2}\right)$-th and $\left(\frac{n}{2} + 1\right)$-th values.
The $\left(\frac{8}{2}\right)$-th value is the 4th value, which is 6.
The $\left(\frac{8}{2} + 1\right)$-th value is the 5th value, which is 8.

The median is: $\boxed{7}$

1.1.4 Calculate the mean for this set

There are 8 marks.

The mean is: $\boxed{6.875}$

1.1.5 Calculate the range for this set

The sorted marks are $4, 5, 6, 6, 8, 8, 8, 10$.
Highest mark = 10
Lowest mark = 4

The range is: $\boxed{6}$