First use the mean to find $x$. Since the mean is 6 for 5 students, the total number of books is $5\cdot 6=30$. The first four values add to $2+4+6+8=20$, so $x=30-20=10$.

Now check the range: the data values are $2,4,6,8,10$. The range is $10-2=8$, which matches the condition.

Next find the standard deviation using the population formula for the full set of 5 values. The mean is 6, so the deviations are:

$2-6=-4$, $4-6=-2$, $6-6=0$, $8-6=2$, $10-6=4$

Square these deviations:

$(-4{)}^2=16$, $(-2{)}^2=4$, $0^2=0$, $2^2=4$, $4^2=16$

The sum of the squared deviations is $16+4+0+4+16=40$. Divide by the number of data values:

$\frac{40}{5}=8$

Take the square root:

$\sqrt{8}$

So the standard deviation is $\sqrt{8}$.

First use the mean to find the missing side length. If the mean of 5 values is 12, then their total is $5(12)=60$. The four known side lengths add to $8+10+14+16=48$, so the missing side length is $60-48=12$. This also fits the given range, since $16-8=8$.

Now the 5 side lengths are $8,10,12,14,16$, with mean 12. Find each distance from the mean: $8-12=-4$, $10-12=-2$, $12-12=0$, $14-12=2$, $16-12=4$. Square these distances: $16,4,0,4,16$. Their sum is $40$.

The standard deviation for this data set is the square root of the average of these squared distances:

So the correct answer is $2\sqrt{2}$.

First find the mean in terms of $x$. The sum of the five numbers is $4+7+9+11+x=31+x$, so the mean is $\frac{31+x}{5}$. Now determine the median. Since the known numbers are $4$, $7$, $9$, and $11$, the median depends on where $x$ falls when the numbers are ordered. Test the answer choices. If $x=14$, the ordered set is $4,7,9,11,14$, so the median is $9$. The mean is $\frac{31+14}{5}=\frac{45}{5}=9$. These are equal, so $x=14$ works. Check the other choices to confirm uniqueness: if $x=9$, mean $=8$ while median $=9$; if $x=11$, mean $=\frac{42}{5}=8.4$ while median $=9$; if $x=15$, mean $=\frac{46}{5}=9.2$ while median $=9$. Therefore, the value of $x$ is $14$.

The mean of the original data set is 18. Adding the same number to every value in a data set increases the mean by that number. Since 4 is added to each of the 5 numbers, the new mean is $18+4=22$. Therefore, the expression that represents the new mean is $18+4$.

Adding the same number to every value in a data set increases the mean by that number but does not change the range. Since each number is increased by 3, the new mean is $14+3=17$. The original range is 10, and because both the maximum and minimum values increase by 3, their difference stays the same: $(\text{max}+3)-(\text{min}+3)=\text{max}-\text{min}=10$. Therefore, the new data set must have mean 17 and range 10.