Fourth Year Homework due Tue 20 Jan, SHOW ALL WORKING OUT. Click pics to enlarge. MARKS: 21.

1. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{No. of petals} & \text{Frequency} & \text{... } \\ \hline \text{3} & 4 & \\ \hline \text{4} & 15 & \\ \hline \text{5} & 22 & \\ \hline \text{6} & 14 & \\ \hline \end{array} Use it to:
   a. Find the mean
   b. Find the median

   [4 marks]

2. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Height in cm} & \text{Freq-Girls} & \text{M.P. $\times$ F} & \text{Freq-Boys} & \text{M.P. $\times$ F} \\ \hline \text{110 $\leq$ h < 115} & 5 & & 11 \\ \hline \text{115 $\leq$ h < 120} & 21 & & 29\\ \hline \text{120 $\leq$ h < 125} & 29 & & 14\\ \hline \text{125 $\leq$ h < 130} & 15 & & 16\\ \hline \end{array} Use it to:
   a. Find separate estimates of the mean for the boys and girls to 4 significant figures
   b. Make a comment comparing boys height to girls using this data.

   [5 marks]

3. HARD: Boat A sails 5 miles on a bearing of $099^\circ$ from Dover. Boat B sails 7 miles on a bearing of $200^\circ$ from Dover. Draw a clear diagram and use it to find the distance between Boat A and Boat B. HINT: you might want to look up the Cosine Rule.

   [4 marks]

4. In triangle XYZ, XY=7cm and YZ=13cm. Angle Y is $54^\circ$, find angle X

   [3 marks]

5. Find angle X to 3 significant figures
   

   [5 marks]