## Stem and Leaf Graphs Exercise

 1. The table shows the areas of 20 highest mountains in Australia and New Zealand.a. Plot this data on a stem and leaf diagram, using the first two digits as the stem. The digits on the leaves should be arranged in order from smallest to biggest.b. Use the diagram to find the median and the upper and lower quartiles of these cave depths.c. Calculate the interquartile range.

 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.