The numbers of matches in 100 boxes are counted and the results are shown in the table below. Calculate the standard deviation. Calculate the mean using class mark. Calculate the mean using assumed mean method, given that the mean is 30.5.

Here are the calculations for the given data.

First, let's organize the data and calculate the necessary values for the mean and standard deviation.

Step 1: Create a table to find class marks ($x$), $fx$, and $fx^2$.
The class mark ($x$) for each interval is the midpoint of the class.
The total frequency $\sum f = 18 + 34 + 37 + 11 = 100$.

Class Interval	Frequency ($f$)	Class Mark ($x$)	$fx$	$x^2$	$fx^2$
25-28	18	$\frac{25+28}{2} = 26.5$	$18 \times 26.5 = 477$	$26.5^2 = 702.25$	$18 \times 702.25 = 12640.5$
29-32	34	$\frac{29+32}{2} = 30.5$	$34 \times 30.5 = 1037$	$30.5^2 = 930.25$	$34 \times 930.25 = 31628.5$
33-36	37	$\frac{33+36}{2} = 34.5$	$37 \times 34.5 = 1276.5$	$34.5^2 = 1190.25$	$37 \times 1190.25 = 44039.25$
37-40	11	$\frac{37+40}{2} = 38.5$	$11 \times 38.5 = 423.5$	$38.5^2 = 1482.25$	$11 \times 1482.25 = 16304.75$
Total	$\sum f = 100$		$\sum fx = 3214$		$\sum fx^2 = 104613$

Step 2: Calculate the mean using class mark (for part ii).
The formula for the mean ($\bar{x}$) of grouped data using class marks is:

$$\bar{x} = \frac{\sum fx}{\sum f}$$

Substitute the values from the table:

$$\bar{x} = \frac{3214}{100}$$ $$\bar{x} = 32.14$$