Calculate the mean, median, and standard deviation for the given grouped frequency distribution.

Here are the calculations for Question 1:

First, we prepare a table to find the midpoints ($x$), $fx$, $fx^2$, and cumulative frequencies ($cf$).
The class intervals are given as 8-12, 13-17, 18-22, 23-27, 28-32. To find the class boundaries, we adjust by 0.5.
The class width ($w$) for each interval is $12.5 - 7.5 = 5$.

Class Interval	Class Boundaries	Midpoint (x)	Frequency (f)	fx	$x^2$	$fx^2$	Cumulative Frequency (cf)
8-12	7.5-12.5	10	6	60	100	600	6
13-17	12.5-17.5	15	8	120	225	1800	14
18-22	17.5-22.5	20	12	240	400	4800	26
23-27	22.5-27.5	25	8	200	625	5000	34
28-32	27.5-32.5	30	6	180	900	5400	40
Total			$\sum f = 40$	$\sum fx = 800$		$\sum fx^2 = 17600$

Total frequency $N = \sum f = 40$.

a) The mean weight

Step 1: Use the formula for the mean of grouped data.

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