|
1. The table shows the areas of 20 highest mountains in Australia and New Zealand. |
 |
|
Name of mountain |
Location |
Height (in metres)
|
|
Malte Brun |
NZ |
3160
|
|
Kosciuszko |
NSW |
2230
|
|
Silberhorn |
NZ |
3300
|
|
Bogong |
VIC |
1990
|
|
Tasman |
NZ |
3500
|
|
Torres |
NZ |
3160
|
|
Jaggungal |
NSW |
2040
|
|
Sefton |
NZ |
3160
|
|
Townsend |
NSW |
2210
|
|
Lendenfeldt
|
NZ
|
3190
|
|
Tate
|
NSW
|
2040
|
|
Cook
|
NZ
|
3750
|
|
Paddy Rushs Bogong
|
NSW
|
1920
|
|
Teichelmann
|
NZ
|
3160
|
|
Perisher
|
NSW
|
2040
|
|
Dampier
|
NZ
|
3440
|
|
Twynham
|
NSW
|
2180
|
|
Gungartan
|
NSW
|
2060
|
|
Hicks
|
NZ
|
3200
|
|
Feathertop
|
VIC
|
1920
|
2. The table below shows the depths of the 15 deepest caves in New Zealand.
|
Name
|
Depth in metres
|
 |
|
Windrift
|
362
|
|
|
Laghu Cave
|
307
|
|
|
Bulmer Cavern
|
749
|
|
|
Nettlebed Cave
|
889
|
|
|
Perseverence Cave
|
315
|
|
|
HH Cave
|
721
|
|
|
Greenlink − Middle Earth
|
394
|
|
|
Incognito / Falcon System
|
540
|
|
|
Blackbird Hole
|
315
|
|
|
Ellis Basin System
|
775
|
|
|
Bohemia Cave
|
713
|
|
|
Harwood Hole
|
357
|
|
|
Viceroy Shaft
|
415
|
|
|
Legless
|
400
|
|
|
Gorgoroth
|
346
|
a. Plot this data on a stem and leaf diagram.
b. Use the diagram to find the median and the upper and lower quartiles of these cave depths.
c. Calculate the interquartile range.
3. The table below shows the length of the top 11 Metro rail transport systems in Europe and North and South America and Asia.
| North and South America and Asia | Europe | ||||
|
City
|
Length (km) |  |
City
|
Length (km)
|
 |
| Mexico City |
178
|
London |
430
|
||
| Washington DC |
144
|
Milan |
72
|
||
| San Francisco |
115
|
Barcelona |
72
|
||
| Toronto |
61
|
Paris |
332
|
||
| Montreal |
64
|
Moscow |
244
|
||
| Boston |
127
|
Madrid |
121
|
||
| New York |
392
|
Berlin |
141
|
||
| Chicago |
173
|
Copenhagen |
170
|
||
| Atlanta |
65
|
Hamburg |
98
|
||
| Tokyo |
244
|
St Petersburg |
92
|
||
| Seoul |
132
|
Stockholm |
110
|
||
a. Draw a back to back stem and leaf diagram.
b. Find the median and quartiles of each distribution.
4. The table shows the lengths of 17 New Zealand rivers in kilometres.
a. Show this information on an ordered stem and leaf diagram, using the first two digits as the stem.
|
River
|
Length
|
River
|
Length
|
River
|
Length
|
River
|
Length
|
 |
|
Waiau |
169 |
Waitaki |
209 |
Mohaka |
172 |
Whangehu |
161 |
|
|
Waiau (Southland) |
217 |
Rangitaiki |
193 |
Oreti |
203 |
Patea |
143 |
|
|
Waimakariri |
161 |
Manawatu |
182 |
Wairau |
169 |
Mokau |
158 |
|
|
Clarence |
209 |
Waihou |
175 |
Rakaia |
145 |
Ngarurora |
154 |
|
|
Buller
|
177
|
|||||||
b. From the stem and leaf diagram find the median, lower quartile and range.
5. The final examination results of two classes are to be compared.
The results are shown below:
|
First class (%)
|
53 |
43 |
67 |
87 |
36 |
56 |
76 |
45 |
87 |
73 |
|
45 |
53 |
74 |
65 |
38 |
71 |
40 |
33 |
59 |
||
|
Second class (%)
|
46 |
45 |
47 |
67 |
56 |
59 |
66 |
50 |
79 |
80 |
|
35 |
55 |
77 |
55 |
30 |
65 |
42 |
39 |
39 |
a. Draw a back to back stem and leaf diagram for the classes.
b. Find the median, quartiles and range.
c. Compare the performances of students in the two classes by commenting on both the centre of the values of each class and their spread.
