The cumulative frequency table shows the speeds of 200 cars. Complete the table and draw the cumulative frequency diagram.

To complete the cumulative frequency table, we need the original frequencies. Based on the previous question (mean calculation), the frequencies are:

• $0 < v \le 20$: 16
• $20 < v \le 40$: 34
• $40 < v \le 45$: 62
• $45 < v \le 50$: 58
• $50 < v \le 60$: 26
• $60 < v \le 80$: 4

Now, calculate the cumulative frequencies:

• For $v \le 20$: 16 (Given)
• For $v \le 40$: $16 + 34 = 50$ (Given)
• For $v \le 45$: $50 + 62 = 112$
• For $v \le 50$: $112 + 58 = 170$
• For $v \le 60$: $170 + 26 = 196$ (Given)
• For $v \le 80$: $196 + 4 = 200$ (Given)

b)

i) The completed cumulative frequency table is:

Speed (v km/h)	Cumulative frequency
$v \le 20$	16
$v \le 40$	50
$v \le 45$	112
$v \le 50$	170
$v \le 60$	196
$v \le 80$	200

To draw the cumulative frequency diagram, plot the upper class boundary against the cumulative frequency.
The points to plot are:

• $(0, 0)$ (starting point)
• $(20, 16)$
• $(40, 50)$
• $(45, 112)$
• $(50, 170)$
• $(60, 196)$
• $(80, 200)$

ii) On the grid:

1. Plot the points listed above.
2. The x-axis (Speed) ranges from 0 to 80, with each small square representing 1 km/h.
3. The y-axis (Cumulative frequency) ranges from 0 to 200, with each small square representing 2 units of frequency.
4. Draw a smooth curve connecting these points, starting from $(0,0)$.