The table shows the weights, to the nearest kilogram, of twelve students in a Further Mathematics class Weight in kg 55 57 59 61 63 No of students 2 1 2 4 3...

(a) Bar chart

(b)(i) Mode

The highest frequency is 4, corresponding to a weight of 61 kg.

\[\boxed{\text{Mode}=61\text{ kg}}\]

(b)(ii) Median

There are \(12\) students. Therefore, the median is the mean of the 6th and 7th observations.

The ordered weights are:

\[55,\ 55,\ 57,\ 59,\ 59,\ \underbrace{61,\ 61}_{\text{6th and 7th}},\ 61,\ 61,\ 63,\ 63,\ 63\]

\[\text{Median}=\frac{61+61}{2}=\boxed{61\text{ kg}}\]

(c) Mean weight

\[\begin{aligned}\sum f&=2+1+2+4+3=12,\\\sum fx&=55(2)+57(1)+59(2)+61(4)+63(3)\\&=110+57+118+244+189\\&=718.\end{aligned}\]

\[\text{Mean}=\frac{\sum fx}{\sum f}=\frac{718}{12}=59.833\ldots\text{ kg}\]

\[\boxed{\text{Mean weight}=60\text{ kg, correct to the nearest kilogram}}\]